Mr Bakiyev has been trying to rally support in his home city
Kyrgyzstan's ousted President Kurmanbek Bakiyev has said he will be willing to step down in return for security guarantees for him and his family.
Mr Bakiyev fled to the south of the country following last week's uprising.
The interim government has yet to give a response to his offer. Its leaders held a late-night meeting in Bishkek, the capital, but made no announcement.
Meanwhile Russian President Dmitry Medvedev warned the country faced civil war if political uncertainty continued.
In a speech in Washington, he said: "Some political leaders will have to make a decision about their fate."
He did not elaborate, but correspondents say the Kremlin has been quick to offer assistance to Mr Bakiyev's rival, Roza Otunbayeva, since she became interim leader.
The interim leaders have lifted Mr Bakiyev's immunity and say they will arrest him if he refuses to surrender.
Rayhan Demytrie, BBC News Bishkek
The opposition interim government has not made up its mind whether to accept the conditions Mr Bakiyev placed on his resignation.
The international community, represented in talks in Bishkek by the OSCE envoy, the UN and the EU special representatives, are trying to convince the interim government to hold talks.
Kyrgyz society, it seems, is also divided. On one hand, we are hearing from the relatives of the victims of the 7 April riots that they want to bring Mr Bakiyev to justice. On the other hand, many feel that the president's resignation would help solve the crisis in the country.
What is interesting is that state channels in Kyrgyzstan are not broadcasting news from the south, where thousands of Mr Bakiyev's supporters have gathered to express their loyalty to him. He has been questioning this, asking: "Where is the democracy and free speech promised by those who seized power?"
Mr Bakiyev previously insisted he remained the legitimate president of Kyrgyzstan.
But at a news conference in his home village of Teyit in Jalalabad, he laid out the conditions under which he would stand down.
He said he wanted "a guarantee that the roaming of these armed people ends in Kyrgyzstan, that this redistribution of property and this armed free-for-all stops", and a guarantee of personal security for himself and his family and relatives.
Mr Bakiyev said the interim government had to "start preparing a snap presidential election to be held within two or three months".
He said he would be prepared to hold talks with Ms Otunbayeva if she travelled to the south to see him.
It was unsafe for him to go to the capital for talks as the administration could not guarantee his security, he said.
Some 5,000 of Mr Bakiyev's supporters, many of them waving banners, gathered in the town in Jalalabad, to hear him speak.
TIMELINE: KYRGYZSTAN UNREST
March 2005: Protests over disputed election, dubbed the Tulip Revolution, lead to fall of President Askar Akayev
July 2005: Kurmanbek Bakiyev elected president by a landslide
October 2007: Referendum approves constitutional changes, which the opposition present as a step towards authoritarianism
December 2007: Bakiyev's Ak Zhol party wins parliamentary poll; opposition left with no seats
July 2009: Bakiyev re-elected in vote criticised by monitors
7 April 2010: Bakiyev ousted in violent protests; interim government takes over
13 April 2010: Interim government removes Bakiyev's immunity from prosecution
The ousted leader also repeated his call for an international investigation to be held into the violent demonstrations last Wednesday, which left more than 80 people dead.
The interim government held a late-night meeting in Bishkek on Tuesday, but did not respond.
However, in an earlier interview Ms Otunbayeva said she was prepared to offer security guarantees to Mr Bakiyev if he resigned and left the country, but would not offer such immunity to his family.
"We will provide security guarantees which he's entitled to under the constitution," she told the Associated Press.
But she warned her patience with Mr Bakiyev was running out.
"His stay in Kyrgyzstan is posing a problem for the nation's future. It's becoming increasingly difficult to guarantee his security as people are demanding to bring him to justice."
The ousted leader's critics have accused him of nepotism for installing his brother and son, among other relatives, in key government posts.
Earlier, Azimbek Beknazarov, a minister in charge of security, said a criminal investigation had been opened against Mr Bakiyev, and that he had until the afternoon to hand himself in to the authorities.
"We can see that the president does not want to step down voluntarily and instead is issuing calls for actions against the people," he said.
The interim government also announced on Tuesday that it had dissolved the country's constitutional court.
Last week's violence was the culmination of weeks of discontent over rising prices and allegations of corruption in Kyrgyzstan.
The interim government has pledged to hold elections in six months' time and says the security forces are under its command.