But it was not immediately clear if Kurmanbek Bakiyev, the president, would agree to Tuesday's compromise deal which would amend the constitution to reduce his powers.
Protesters camped out in a square in the capital demanding the president's resignation on Tuesday and said they would remain there until they were convinced the agreement would hold.
However, by Wednesday morning only a few hundred of protesters remained in the square.
In previous days, several thousand people had demonstrated against the president who they said had failed to tackle corruption or carry out promised economic reforms.
The political crisis has destabilised Kyrgyzstan, a strategically important part of the resource-rich Central Asia region where China, Russia and the US jostle for influence.
Violence erupted for the first time on Tuesday when riot police used tear gas to break up fighting between a group of opposition supporters and pro-government protesters.
Six people were taken to hospital, the health ministry said.
After hours of talks in parliament, opposition and pro-government politicians said on Tuesday they had agreed on a compromise draft of a new constitution that would reduce presidential powers.
The proposed draft would strip the president of his right to dissolve parliament, and give parliament the power to appoint the prime minister and cabinet.
Kanybek Imanaliyev, an opposition leader, said: "We have chosen to go down the path of a parliamentary-presidential form of government.
"I have been speaking in the square with our members of parliament. They are convincing our supporters that we have reached agreement and they should go home quietly."
No comment from Bakiyev
Bakiyev came to office on a wave of popular enthusiasm
Bakiyev's office made no comment on the deal. But if two thirds of the 75-seat chamber approve the new constitution, under law the president will have to accept it.
Bakiyev came to power last year after rioting in the capital forced his predecessor to flee. He was elected soon after on a promise of thorough reform.
Opposition leaders say he has backtracked on that commitment and allowed his administration to become mired in corruption and nepotism.