This is a key demand by the opposition, who has warned that parliament’s failure to act now will further inflame mass anti-government protests.
Pro-presidential MPs oppose the move, and the speaker has given until Wednesday morning to find a compromise.
Kiev’s decision to reject an EU deal in November triggered the protests.
At least six people have died in violence since then, and a number of Ukrainian politicians have warned that the country might plunge into civil war.
The opposition is pushing for a return to the 2004 constitution, which would mean President Viktor Yanukovych losing some of the powers he has gained since his election in 2010.
The changes envisage that parliament – not the president – will be appointing the prime minister and cabinet members as well as regional governors.
There were emotional scenes earlier on Tuesday and MPs began debating the issue.
“I call on everyone to take the constitutional route and stop dictatorship,” the leader of the opposition Udar (Punch) Party and former world heavyweight boxing champion, Vitaliy Klitschko, told parliament.
“Let us reinstate the constitution that allows MPs to take decisions instead of just pushing buttons.”
Vitaliy Klitschko also stressed that snap presidential elections were crucial to regain the trust of the people.
But the leader of President Viktor Yanukovych’s Regions Party in parliament, Oleksandr Yefremov, accused the opposition of being irresponsible.
“They [opposition leaders] are fighting not for what people want, but for power,” he said in a speech delivered amid shouting.
“Ukraine is going through perhaps the most dramatic period in its recent history. Any further escalation of the conflict may lead to civil confrontation and result in catastrophic consequences,” he added.
At one point during the proceedings, some opposition MPs shouted “murderers!”.
They were referring to the death of protesters over recent weeks as anti-government activists clashed with riot police.
Protesters blame the government for the deaths, but officials reject these accusations.
Later on Tuesday, the speaker of parliament, Volodymyr Rybak, gave lawmakers until 10:00 local time on Wednesday to try to find a compromise on the constitutional changes.
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