Forty-five of the chamber's 71 deputies agreed to create the new body.
RFE/RL's Kyrgyz Service reports that by 1:30 a.m. local time today, 36 lawmakers had signed an agreement in support of a draft constitution supported by most opposition groups that would cut Bakiev's powers.
The remaining signatories were expected by noon today.
After the agreement was signed, Kyrgyz lawmaker Kanybek Imanaliev addressed the cheering crowd of around 5,000 people gathered in front of the parliament building.
"We, starting from this hour, and starting from this minute, have launched a new constitution's epoch," he said. "We will finish it [when] the rest [of the] deputies sign it [in the] morning. For the new constitution!"
He then shouted, "For the new Kyrgyzstan! For a new president!" to the cheers of the crowd.
MORE: A gallery of images from today's demonstrations in Bishkek.
Coverage of the unrest in Kyrgyz from RFE/RL's Kyrgyz Service.
RFE/RL's Kyrgyz Service reports that the crowd then began dispersing. Some people remained in the tents they had erected earlier on the square.
Protesters have been picketing Bakiev's administration for days to press for constitutional reforms that would give parliament greater powers.
The decision to create a Constituent Assembly was made around 1 a.m. this morning, when Cholpon Bayekova -- the head of the Constitutional Court -- told members of parliament that the Kyrgyz constitution does not contain a provision to adopt a new constitution. For that to happen, she said, a new body first needed to be established.
The deputies present then agreed to set up a Constituent Assembly. Opposition lawmaker Kubatbek Baibolov was elected its chairman.
A message was sent to Bakiev and Prime Minister Feliks Kulov, but there was no immediate reaction.
Emergency Session Convened
Kyrgyz lawmakers started gathering in the parliament's building after nightfall following opposition calls for an emergency session of the legislature.
RFE/RL Kyrgyz Service correspondents reported from inside the parliament building that 45 lawmakers out of the 51 required to make a quorum were present by 12:45 a.m. local time on November 7. Parliament Speaker Marat Sultanov was trying to get the remainder to come and attend the session.
Parliamentarians also wanted President Bakiev, Prime Minister Kulov, and Constitutional Court Chairwoman Cholpon Baekova to attend.
Meanwhile, crowds of demonstrators estimated as large as 40,000 people thronged the streets of the capital, according to RFE/RL's Kyrgyz Service.
Riot police observe the demonstration in Bishkek today (RFE/RL)
Opposition lawmaker Temir Sariev told RFE/RL earlier the session was intended, among other things, to discuss a draft constitution that would ensure a more even balance between the executive and legislative branches of government.
Earlier today, Bakiev submitted to parliament his own proposed amendments to the existing constitution.
But instead of bringing them personally, as he had said he would do, he dispatched Alymbay Sultanov, his representative in parliament. Opposition lawmakers left the parliament's building in protest, thus disrupting the session.
Talking to Russian journalists afterward, Bakiev criticized his opponents.
"I had said before that on the 6th [of November] I would bring my proposals for changes and additions to the constitution and I did it," Bakiev said. "This morning my own project was brought to parliament. But they didn't pay any attention, and instead of beginning to review [my draft] they continue to insist that the president and the prime minister resign."
Administration Defends Bakiev's Ideas
State Secretary Adakhan Madumarov told reporters that Bakiev's proposals aim to create a mixed presidential-parliamentary form of government.
Madumarov said that under the amended constitution the legislature would have greater powers, including the right to appoint the prime minister. He also claimed the changes would restrict the president's ability to dissolve parliament.
"[The president is proposing] a consensual form of government,"' Madumarov said. "I think that all two, three, four sides involved [in the discussion], as well as some political parties, have agreed that Kyrgyzstan should have a presidential-parliamentary form of government. This is what has been sent [today] to parliament for reviewing."
Bakiev's opponents reacted harshly to Bakiev's initiative, saying it would only deepen the ongoing political crisis.
Lawmakers Reject Proposed Amendments
Addressing protesters gathered in front of the White House today, opposition lawmaker Omurbek Babanov accused the president of deception.
"The president has submitted a project that is worse than the current constitution," Babanov said. "That's how he's listening to us! What he proposes is a super-presidential constitution. We won't let [him] do that. Bakiev should go!"
Another opposition leader, Social Democrat Party leader Almazbek Atambaev, expressed similar criticism.
"Unfortunately, instead of bringing a new draft constitution that would restrict the rights of [his] family clan, President Kurmanbek Salievich Bakiev today submitted a totally different draft," Atambaev said. "His draft makes the existing constitution even worse. It will make the country even more dependent on one single individual who, as we see, is surrounded by not very recommendable people. It is a great misfortune for the country."
Parliament Speaker Sultanov also dismissed the president's proposals.
"We thought the president would come out with democratic proposals that would restrict his powers," he said. "But they restrict his prerogatives with regard to only one thing, that is the nomination of the prime minister. For the rest, it strengthens the presidential powers."
Bishkek Demonstrations Grow
Following news that Bakiev's proposals did not meet the opposition's demands, the number of protesters outside the White House greatly increased.
Earlier in the day, the protesters were joined by Turgunbek Kulmurzaev, the governor of Chui Oblast, which includes the city of Bishkek.
Demonstrators in Bishkek today (RFE/RL)
As tensions rose during the day, presidential administration head Myktybek Abdyldaev appeared before the crowd and read out a presidential decree removing acting Interior Minister Osmanali Guronov from office.
Abdyldaev said the president had put Guronov's deputy, Omurbek Subanaliev, temporarily in charge of the ministry.
Addressing the demonstrators, Subanaliev pledged not to use force against them.
He also promised to sack Bishkek police chief Moldomusa Kongantiev, the brother of Kyrgyz Prosecutor-General Kambaraly Kongantiev.
Moldomusa Kongantiev's removal was one of the demands of the opposition.
Some opposition leaders, however, dismissed the reshuffle as merely a tactical move by Bakiev.
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