Two of the groups that attended the meeting said this was only a first step in a dialogue which has yet to meet their central demand - the immediate ouster of longtime President Hosni Mubarak.
"People still want the president to step down," said Mostafa al-Naggar, a protest organizer and supporter of Mohamed ElBaradei, a Nobel Peace laureate and one of the country's leading democracy advocates.
"The protest continues because there are no guarantees and not all demands have been met," he added. "We did not sign on to the statement. This is a beginning of a dialogue. We approve the positive things in the statement but ... we are still demanding that the president step down."
The outlawed Muslim Brotherhood, the country's largest opposition group, made a similar statement after its representatives attended the meeting.
Vice President Omar Suleiman offered to set 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 also included a pledge not to harass those participating in anti-government protests, which have drawn hundreds of thousands at the biggest rallies. The government agreed not to hamper freedom of press and not to interfere with text messaging and Internet.
The 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."
Mubarak is insisting he cannot stand down now or it would only deepen the chaos in his country. The United States shifted signals and gave key backing to the regime's gradual changes on Saturday, warning of the dangers if Mubarak goes too quickly.
Sunday's meeting drew the broadest representation of Egypt's fragmented opposition to sit with the new vice president since the protests began on Jan. 25.
The new offer of concessions followed a series of others that would have been unimaginable just a month ago in this tightly controlled country. All appear geared to placate the protesters and relieve international pressure without giving in to the one demand that unites all the opposition - Mubarak's immediate departure. The latest agreement makes no mention of any plan for Mubarak to step before a new election is held later this year.
Since protests began, Mubarak has pledged publicly for the first time that he will not seek re-election. The government promised his son Gamal, who had widely been expected to succeed him, would also not stand. Mubarak appointed a vice president for the first time since he took office three decades ago, widely considered his designated successor. 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.
There were signs that the paralysis that has gripped the country since the crisis began was easing Sunday, the first day of the week in Egypt. Some schools reopened for the first time in more than a week, and banks did the same for only three hours with long lines outside. However, there is still a night curfew, and tanks ringing the city's central square and guarding government buildings, embassies and other important institutions.
At the epicenter of the protests, Tahrir (Liberation) Square in central Cairo, some activists said they had slept under army tanks ringing the plaza for fear they would try to evict them or further confine the area for demonstrations. The crowd of thousands in the morning swelled steadily over the day to tens of thousands in the late afternoon. Many were exhausted and wounded from fighting to stand their ground for more than a week in the square.
"We are determined to press on until our number one demand is met," said Khaled Abdul-Hameed, a representative of the protesters.
He said the activists have formed a 10-member "Coalition of the Youths of Egypt's Revolution," to relay their positions to politicians and public figures negotiating with the regime.
"The regime is retreating. It is making more concessions everyday," Abdul-Hameed said.
The opposition groups represented at the meeting included the youthful supporters of ElBaradei, who are one of the main forces organizing the protests. ElBaradei was not invited and his brother said the statement by those who did attend does not represent his personal view.
The Muslim Brotherhood and a number of smaller leftist, liberal groups also attended, according to footage shown on state television.
The government offered to open an office that would field complaints about political prisoners, according to the state news agency. It also pledged to commission judicial authorities to fight corruption and prosecute those behind it. In another concession, authorities promised to investigate and prosecute those responsible for the yet unexplained disappearance of police from Cairo's streets more than a week ago, which unleashed a wave of lawless looting and arson.
The government agreed to set up a committee that includes public and independent figures and specialists and representatives of youth movements to monitor the "honest implementation" of all the new agreements and to report back and give recommendations to Suleiman.
"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 Muslim Brotherhood representative Issam Aryan
Mohammed Mursi, one of the Brothers who attended the talks, said: "Unless he moves fast to meet people's demands there is no point in the dialogue."
Mursi said what was issued was a position in principle, "a first step."
"All those attending the meeting agreed the protesters have a right to stay where they are without anyone assaulting them," he said. "People want real change, a change that includes the president, his government, his party and his regime," Mursi added.
He also said the group was expecting a second round of talks within a few days.
The fundamentalist Muslim Brotherhood, which has been outlawed since 1954 but fields candidates in parliamentary elections as independents, did not organize or lead the protests currently under way and only publicly threw its support behind them a few days into the movement. It only ordered its supporters to take part when it sensed that the protesters, mostly young men and women using social networks on the Internet to mobilize, were able to sustain their momentum.
There have been no known discussions between the Brotherhood and the regime in years - one of many startling shifts in policy after years of crackdowns by the Western-backed regime against the Islamists.
Both Mubarak and Suleiman have blamed the Brotherhood as well as foreigners of fomenting the recent unrest. Mubarak is known to have little or no tolerance for Islamist groups and the decision to open talks with the Brotherhood is a tacit recognition by his regime of their key role in the ongoing protests as well as their wide popular base.
The Brotherhood aims to create an Islamic state in Egypt, but insists that it would not force women to cover up in public in line with Islam's teachings and would not rescind Egypt's 1979 peace treaty with Israel.
The group, which fields candidates as independents, made a surprisingly strong showing in elections in 2005, winning 20 percent of parliament's seats. However, thousands of its members were arrested in crackdowns over the past decade and it failed to win a single seat in elections held late last year. The vote was heavily marred by fraud that allowed the National Democratic Party to win all but a small number of the chamber's 518 seats.
At Tahrir Square, 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," he said.
In the capital Cairo, home to some 18 million people, there were some signs of a return to normalcy. Traffic was back to near regular levels and more stores reopened across the city, including some on the streets leading to Tahrir Square. Protesters greeted some store owners and people returning to work with flowers.
In Zamalek, an affluent island in the middle of the Nile that is home to many foreign embassies, food outlets reopened and pizza delivery boys checked their motorbikes. Employees at a KFC restaurant wiped down tables. Hairdressers and beauty salons called their patrons to let them know they were reopening.
Associated Press reporter Salah Nasrawi contributed to this report from Cairo.