Leonid Kravchuk, president from 1991 to 1994, opened the debate in parliament by urging everyone involved to "act with the greatest responsibility".
President Viktor Yanukovych wants any amnesty to be conditional on protesters leaving official buildings - a proposal rejected by the opposition.
They want Mr Yanukovych to resign.
Hundreds of anti-government protesters - many wearing helmets and carrying baseball bats and other makeshift weapons - have taken to the streets in Kiev again, a BBC correspondent in the city reports.
They won significant concessions on Tuesday after parliament scrapped a controversial anti-protest law and Prime Minister Mykola Azarov and his cabinet resigned.
Leonid Kravchuk told MPs that "all the world acknowledges and Ukraine acknowledges that the state is on the brink of civil war".
"It is a revolution. It is a dramatic situation in which we must act with the greatest responsibility," he said in an emotional address that earned him a standing ovation.
"We need to ease the confrontation between the sides and agree a plan to solve the conflict. We need to work on this plan step by step to ease the confrontation."
To underline the importance of the session, former presidents Leonid Kuchma and Viktor Yushchenko were also present.
Parliament is considering an amnesty for the scores of protesters who have been detained since demonstrations began in November.
Adjourning the session for a break, speaker Volodymyr Rybak admitted there were "several unresolved issues" but said discussions between the two sides would continue.
In an emergency debate on Tuesday, MPs voted to repeal anti-protest legislation, which among other measures banned the wearing of helmets by protesters and the blockading of public buildings.
The anti-protest law, passed less than two weeks earlier, fuelled major protests around the country and deadly clashes with the police.
Prime Minister Azarov said on Tuesday he was stepping down to create "social and political compromise".
He has been replaced on an interim basis by his deputy, Serhiy Arbuzov.
Correspondents say Mr Azarov was deeply unpopular with the opposition, who accused him of mismanaging the economy and failing to tackle corruption.
Members of Mr Azarov's cabinet also resigned, but they can remain in their posts for 60 days until a new government is formed.
Both US President Barack Obama and German Chancellor Angela Merkel have underlined their support for the demonstrators.
Mrs Merkel told the German parliament the demonstrators are "fighting for the same values that also guide us, the European Union, and that is why they need to be listened to."
Mr Obama, in his State of the Union address, said:
"In Ukraine, we stand for the principle that all people have the right to express themselves freely and peacefully, and have a say in their country's future."
The White House on Tuesday said Vice-President Joe Biden had spoken by telephone to President Yanukovych and praised the "progress made".
Meanwhile, both the European Union's High Representative for Foreign Affairs, Catherine Ashton, and Enlargement Commissioner Stefan Fuele have arrived in Kiev for talks with the leadership.
Russia's President Vladimir Putin on Tuesday criticised what he called foreign "interference" in Ukraine, saying:
"I think that the Ukrainian people are capable of solving this on their own."
"I can only imagine how our European partners would respond if in the heat of a crisis in a country like Greece or Cyprus, our foreign minister would appear at one of their anti-European rallies and begin addressing them," he said at the end of an EU-Russia summit in Brussels.
Protests have spread in recent days across Ukraine - even to President Yanukovych's stronghold in the east - and official buildings in several cities have been occupied.
At least five people have been killed in violence linked to the protests.
Mr Yanukovych was democratically elected in 2010 and appeared to be steering the former Soviet state towards EU integration until he rejected a planned trade deal with the bloc just days before it was due to be signed last November.
His decision to favour instead a $15bn (£9bn) bailout from Russia to bolster the ailing public finances angered many EU supporters in Ukraine.
Ukraine unrest - key dates
- 21 Nov 2013: Ukraine announces it will not sign a deal aimed at strengthening ties with the EU
- 30 Nov: Riot police detain dozens of anti-government protesters in a violent crackdown in Kiev
- 17 Dec: Russia agrees to buy $15bn of Ukrainian government bonds and slash the price of gas it sells to the country
- 16 Jan 2014: Parliament passes law restricting the right to protest
- 22 Jan: Two protesters die from bullet wounds during clashes with police in Kiev; protests spread across many cities
- 25 Jan: President Yanukovych offers senior jobs to the opposition, including that of prime minister, but these are rejected
- 28 Jan: Parliament votes to annul protest law and President Yanukovych accepts resignation of PM and cabinet