But the opposition leaders held firm to a demand the government rejects: that President Hosni Mubarak step down immediately. And the source of the opposition's sudden power - the youthful protesters filling Cairo's main square - said they weren't even represented at the talks and won't negotiate until Mubarak is gone.
"None of those who attended represent us," said Khaled Abdul-Hamid, one leader of a new coalition representing at least five youth movements that organized the 13-day-old protests. "We are determined to press on until our number one demand is met" - the ouster of Mubarak.
"The regime is retreating," Abdul-Hamid told The Associated Press. "It is making more concessions every day."
At the same time, there were signs that the paralysis gripping the country since the crisis began was easing Sunday, the first day of Egypt's work week. Some schools reopened for the first time in more than a week, and so did banks - though for only three hours, with long lines outside. A night curfew remains, and tanks continue to ring the city's central square and guard government buildings, embassies and other important institutions.
Since protests began Jan. 25, the 82-year-old Mubarak has pledged not to seek another term in elections to be held in September. The government promised that his son Gamal, who had widely been expected to succeed him, will not do so. Mubarak appointed a vice president - Omar Suleiman - for the first time since he took office three decades ago. He sacked his Cabinet, named a new one and promised reforms. And on Saturday, the top leaders of the ruling party, including Gamal Mubarak, were purged.
Sunday brought another concession that would have been unimaginable just a month ago in this tightly controlled country: Suleiman's meeting with opposition groups including the fundamentalist Muslim Brotherhood, which has been outlawed since 1954 but is the ruling party's largest rival.
Egypt's opposition - essentially banned by the government for decades - has long been hampered by a lack of cohesiveness. Sunday's talks could be a sign the government is trying to divide and conquer as it tries to placate protesters without giving in to their chief demand.
Mubarak is insisting he cannot stand down now or it would only deepen the chaos in his country. The protesters, skeptical of a regime they blame for repression, corruption and widespread poverty, vow to maintain their pressure until Mubarak leaves.
The United States gave key backing to the regime's gradual changes on Saturday, after President Barack Obama signaled more strongly that it was time for Mubarak to leave. On Sunday, speaking to Fox News ahead of the Super Bowl football broadcast, Obama said he would not be drawn into predicting when Mubarak would leave office.
"Only he knows what he's going to do," Obama said.
Obama said he hopes to see a representative government emerge and played down concerns that Egypt could become hostile to U.S. interests if the Muslim Brotherhood becomes the dominant political force.
"I think that the Muslim Brotherhood is one faction in Egypt," Obama said. "They don't have majority support."
The Brotherhood and another group that attended Sunday's talks said afterward that they were only a first step in a dialogue which has yet to meet their central demand for Mubarak's immediate ouster.
"I think Mubarak will have to stop being stubborn by the end of this week because the country cannot take more million strong protests," said Brotherhood representative Essam el-Erian.
Suleiman, who is leading the government's management of the crisis, offered a series of new concessions, saying the government would no longer hamper freedom of press and won't interfere with text messaging or the Internet.
He proposed setting up a committee of judiciary and political figures to study proposed constitutional reforms that would allow more candidates to run for president and impose term limits on the presidency, the state news agency reported. The committee was given until the first week of March to finish the tasks.
The offer included a pledge not to harass those participating in anti-government protests, which have drawn hundreds of thousands at the biggest rallies.
One of the biggest fears of protesters is that if Mubarak or his close confidant Suleiman remain in power, they will exact revenge for the humiliating demonstrations by rounding up protesters and torturing them. Many protesters have reported seeing undercover security forces in the crowds every day, photographing the demonstrators with cell phone cameras.
Suleiman's offer to eventually lift emergency laws with a major caveat - when security permits - would fulfill a longtime demand by the opposition. The laws were imposed by Mubarak when he took office in 1981 and they have been in force ever since. They give police far-reaching powers for detention and suppression of civil and human rights.
Senate Foreign Relations Committee Chairman John Kerry hailed the talks with opposition groups and the promise to remove the emergency law as "frankly quite extraordinary." Kerry called on Mubarak to lay out a timetable for transition and new elections.
"He must step aside gracefully, and begin the process of transition to a caretaker government. I believe that is happening right now," Kerry told NBC's Meet the Press. "What's needed now is a clarity in this process."
Suleiman also offered to open an office that would field complaints about political prisoners, according to the state news agency. He promised measures to fight corruption and to prosecute those responsible for the unexplained disappearance of police from Cairo's streets more than a week ago. And the government agreed to set up a committee including independent figures and members of the youth movement to monitor the "honest implementation" of all the new agreements.
Some prominent figures from Egypt's elite have suggested that there is a deliberate attempt by the regime to cling to power by offering just enough to satisfy some established opposition groups like the Brotherhood.
Abouel Ela Madi, an ex-Brotherhood member, said the regime hopes to draw the group away from the other protesters.
"If the regime manages to influence the Brotherhood, it will have a shattering effect. A bulk of the protesters belong to the Brotherhood and thus their talks might play a negative role in foiling the completion of the revolution," he said. "I hope they don't make this mistake."
Of all the opposition groups that met with Suleiman, the Brotherhood stands to gain the most. There have been no known discussions between the group and the regime at this level since Mubarak took power in 1981.
The Brotherhood won 20 percent of parliament's seats in 2005 by fielding candidates as independents, but thousands of its members were arrested in crackdowns over the past decade and it failed to win a single seat last year in elections that were marred by fraud.
The Brotherhood's potential rise is a key concern of the U.S. and Israel, countries that have depended on Mubarak as an ally in the Arab world. The Brotherhood aims to create an Islamic state in Egypt but insists it would not rescind Egypt's 1979 peace treaty with Israel and would not take hardline measures such as forcing women to cover up in public.
The Brotherhood did not organize or lead the protests currently under way. It ordered its supporters to take part a few days after they began, sensing that the protesters, mostly young men and women using social networks on the Internet to mobilize, were able to sustain their momentum. Now the Brotherhood's followers appear to be growing in Cairo's Tahrir Square, the epicenter of the uprising.
Suleiman and Mubarak have both blamed the Brotherhood for fomenting the unrest, which turned violent for a time early last week when Mubarak supporters tried to push protesters out of the square. But opening talks with the Brotherhood is a tacit recognition by the regime of its role in the ongoing protests as well as its wide popular base.
Along with the Muslim Brotherhood, a number of smaller leftist, liberal groups also attended, according to footage shown on state television. Most are little-known groups that were around before the protests began.
Mohammed Mursi, a member of the Brotherhood who attended the talks, said a second round of talks is expected within a few days.
Some of the youthful supporters of Mohamed ElBaradei, a Nobel Peace laureate and one of the country's leading democracy advocates, were among those who participated. However, ElBaradei himself was not invited and his brother said the statement by those who did attend does not represent his personal view. ElBaradei is among those refusing to talk to representatives of Mubarak until he steps down.
"The process is opaque," ElBaradei told NBC's Meet the Press. "Nobody knows who is talking to whom at this stage."
Protesters in Tahrir Square numbered in the thousands Sunday morning and swelled steadily to tens of thousands by the late afternoon. Many were exhausted and wounded from fighting to stand their ground for more than a week.
Hundreds performed the noon prayers and later offered a prayer for the souls of protesters killed in clashes with security forces. Later, Christians held a Sunday Mass and thousands of Muslims joined in.
Some of the worshippers broke down and cried as the congregation sang: "Bless our country, listen to the screams of our hearts."
"In the name of Jesus and Muhammad we unify our ranks," Father Ihab al-Kharat said in his sermon. "We will keep protesting until the fall of the tyranny."
Elsewhere in this city of some 18 million people, life took a few steps toward normalcy. Traffic was close to regular levels and more stores reopened, including some on the streets leading to Tahrir Square. Protesters greeted some store owners and people returning to work with flowers.
Associated Press reporter Salah Nasrawi contributed to this report from Cairo.