The protestors responded hurling rocks and setting fires. They want an end to corruption, police abuse and unemployment, reports CBS News correspondent Elizabeth Palmer.
There were signs that the crackdown on protesters was taking a toll on Egypt's international standing. In Washington, White House Spokesman Robert Gibbs would not say whether President Hosni Mubarak, the target of demonstrators' anger and a close U.S. ally, still has the Obama administration's support. Secretary of State Hillary Clinton said the government should allow peaceful protests instead of cracking down.
"We are particularly hopeful that the Egyptian government will take this opportunity to implement political, economic and social reforms that will answer the legitimate interests of the Egyptian people," Clinton said. She appealed to Egypt's leaders to heed calls to open political space for dissent and improve conditions that have led to widespread poverty and unemployment.
The latest deaths brought to six the number of people killed in two days of protests.
Security officials said a total of 860 protesters have been rounded up nationwide since Tuesday, when tens of thousands turned out for the largest protests in Egypt in years - inspired by the uprising in Tunisia. They demanded Mubarak's ouster and a solution to grinding poverty, rising prices and high unemployment.
"What happened yesterday was a red light to the regime. This is a warning," businessman Said Abdel- Motalib said on Wednesday.
From a vantage point overlooking the main Tahrir square, American eyewitness Alex Ortiz reported the presence of about 10 troop carriers and riot police. The square still has normal traffic though the security presence is impossible to miss.
Security forces and plainclothes policemen were visible all over the center of the city, according to Ortiz.
Live Video from Eyewitness Alex Ortiz in Cairo
After nightfall Wednesday, more than 2,000 demonstrators were marching on a major downtown boulevard along the Nile when dozens of riot police with helmets and shields charged the crowd. Other smaller clashes carried on late into the night around the capital. In one of them, protesters stoned police, who fired back with tear gas from one of the main bridges over the Nile.
Though Wednesday's demonstrations were much smaller, it was significant that protesters were able to sustain the movement over two days given the heavy handedness police have shown and the Interior Ministry's warning that there would be zero tolerance for any more unrest.
They were the latest in outbursts of political discontent in Egypt that have been growing more frequent and more intense over the past year. Protests have erupted sporadically over police brutality, poverty and food prices, government corruption and mismanagement, and more recently sectarian strife between Christians and Muslims. Parliamentary elections in November were widely decried as fraudulent.
Many in Egypt see these events as signs of the authoritarian president's vulnerability in an election year. There is speculation that 82-year-old Mubarak, who has been in power for nearly 30 years and recently experienced serious health problems, may be setting his son Gamal up for hereditary succession. But there is considerable public opposition and, according to leaked U.S. diplomatic memos, it does not meet with the approval of the powerful military. And the regime's tight hold on power has made it virtually impossible for any serious alternative to Mubarak to emerge.
also spread Wednesday claiming Mubarak's son had fled the country. However, sources tell CBS News this is not true.
European leaders had harsh words for Egypt and expressed concern, saying the events underlined the need for democratization and respect for human and civil rights.
Activists used social networking sites to call for fresh demonstrations Wednesday. But Facebook, a key tool used to organize protests, appeared to be at least partially blocked in the afternoon. On Tuesday, Twitter and cell phones appeared to be sporadically blocked as well.
The Interior Ministry warned Wednesday that police would not tolerate any gatherings, and thousands were out on the streets poised to crack down quickly on any new signs of unrest after clashes on Tuesday that killed three demonstrators and one police officer.
Early Wednesday, thousands of policemen in riot gear and backed by armored vehicles took up posts in Cairo on bridges across the Nile, at major intersections and squares as well as outside key installations such as the state TV building and the headquarters of Mubarak's ruling National Democratic Party.
Police fired tear gas to disperse a crowd of several hundred activists on a main commercial thoroughfare in central Cairo, chasing them through side streets as both sides pelted each other with rocks with hundreds of onlookers watching anxiously. Plainclothes officers shoved some into waiting vans, slapping them in the face. Protesters hurled rocks at police trucks and set tires and trash on fire as they marched.
Protesters also attacked a military vehicle, smashing its windows and hurling rocks at a couple of green police trucks.
The day's demonstrations began when dozens gathered outside the Journalists' Union in downtown Cairo and renewed the chants heard against Mubarak throughout Tuesday's much larger protests. "Mubarak is leaving, leaving. O Egyptian people, be brave and join us," they chanted. As police charged the crowd, beating them with sticks, they chanted "peaceful, peaceful."
At some of the trouble spots, plainclothes policemen have been ordering passengers on Cairo's ubiquitous minibuses to clear out and then quickly filling them up with detained protesters.
In the city of Suez east of Cairo, an angry crowd of about 1,000 people gathered outside the city's morgue demanding to take possession and bury the body of one of three protesters who died in clashes on Tuesday. The crowd later clashed with riot police and the two sides pelted each other with rocks. Protesters also threw firebombs at police, who responded with rubber bullets and tear gas.
Later, about 300 protesters laid siege to a police station in the city's downtown, throwing rocks. Police responded by firing live ammunition in the air.
"We don't have jobs and now we don't have peace," lamented Zeinab Abdullah, a 45-year-old government employee, who left work early to watch protests in Suez. "There is no way people will be quieted after this. The people of Suez will get angrier and angrier. That is a guarantee."
In the southern city of Assiut, eyewitnesses said riot police set upon some 100 activists staging an anti-government protest Wednesday, beating them up with batons and arresting nearly half of them.
"Down, down Hosni Mubarak," chanted the crowd. "Oh, people, join us or you will be next."
There were protests in at least three other locations across Egypt.
At least eight journalists have been arrested in the troubles. Police arrested an Associated Press Television News cameraman and his assistant early Wednesday while they were filming clashes in Cairo. An AP photographer was beaten by a policeman and had his cheekbone fractured while shooting demonstrations late Tuesday.
Wednesday's two deaths - one policeman and one protester hit by rocks during a protest in a poor central Cairo neighborhood - take to six the number of people who died so far in the clashes. Earlier, three protesters in Suez and one policeman in Cairo died.
Many protesters say they have been inspired by the uprising in Tunisia - even invoking some of the identical slogans heard in the other north African nation.
On Tuesday, protesters clashed with police, who used rubber bullets, water cannons, tear gas and truncheons to disperse them.
Security officials said up to 200 protesters were detained early Wednesday in this Arab nation of some 80 million people. More were likely to be detained as authorities review police video tapes of the protests, the officials said, speaking on condition of anonymity because they were not authorized to speak to the media.
European reaction to the crackdown was critical. German Foreign Minister Guido Westerwelle said he was "very concerned" and called on all concerned to show restraint.
"The situation in Egypt must not escalate," he said. "The current situation in Egypt ... underlines the necessity of democratization, of respect for human and civil rights," Westerwelle told reporters in Berlin, pointing to the need for freedom of opinion, assembly and the press to be respected.
"We are seeing in the last few weeks that a country's stability is not endangered by granting civil rights - it is through the refusal of civil and human rights that societies become unstable," he said in a reference to Tunisia.
The European Union said Egyptian authorities should listen to their people, deal with their problems and respect their right to demonstrate. The office of EU foreign affairs chief Catherine Ashton urged "Egyptian authorities to respect and to protect the right of Egyptian citizen to manifest their political aspirations."
Protesters have vented anger over a host of ills in Egyptian society.
Nearly half of all Egyptians live under or just above the poverty line, set by the World Bank at $2 a day. The widespread poverty, high unemployment and rising food prices pose a threat to Mubarak's regime at a time when tensions between Muslims and Christians are adding to the nation's woes.
A parliamentary election marred by allegations of widespread fraud that saw Mubarak's ruling National Democratic Party win all but a small number of the chamber's 518 seats.
In recent weeks, Mubarak and his son have repeatedly vowed to ensure that ambitious economic reforms engineered by the younger Mubarak over the past decade filter down to the poor. But that has not happened and there has been a marked increase in the frequency of street protests over the economy.
Egypt's benchmark stock index tumbled more than 6 percent by close Wednesday, the lowest level in about eight months and the first concrete sign that the demonstrations have impacted the country's economy.
The city is saturated with tens of thousands of police, but in spite of the heavy-handed tactics, the demonstrators show no sign of backing down, according to Palmer.