More than 80 people were killed in the unrest that led Bakiyev to escape to his power base in the south and Medvedev warned that Kyrgyzstan could turn into a "second Afghanistan" if the subsequent political deadlock is not resolved.
"The risk of Kyrgyzstan breaking apart - into the south and the north - really exists," he said during a speech at Brookings Institution think-tank.
Bakiyev has said he is ready to resign as long as his safety is guaranteed.
"In what case would I resign? First of all, they should guarantee that in Kyrgyzstan there are no more people walking around with weapons, and no seizures or redistribution of property," he told reporters on Tuesday.
"Also, I need to know that my own security and the security of members of my family and those close to me will be assured."
Al Jazeera's Roza Ibragimova, reporting from the capital, Bishkek, described the situation as a "deadlock".
"I've just spoken to the chief of staff of Roza Otunbayeva [self-declared interim leader], Edil Baisalov. He told me Bakiyev's conditions are not new.
"They're not really interested in hearing anything more from Bakiyev but he also said they're still talking to him indirectly through media organisations and international organisations.
"So, [the interim government] still wants to find a way out of this without letting the situation escalate further, not letting the country decent into chaos and more violence.
Otunbayeva told the Associated Press news agency that her government would offer security if Bakiyev stepped down and left the country.
"We will provide security guarantees which he's entitled to under the constitution," she said.
But there was no such offer for his family.
Reports on Tuesday suggested that a convoy of military vehicles was on its way to Jalal'abad in the south, where Bakiyev has been rallying suporters, and that his immunity from arrest had been removed.
But the interim government's chief of staff told the AFP news agency that Otunbayeva has not yet signed any document ordering the arrest of Bakiyev.
A court has, however, issued a warrant for Bakiyev's brother and eldest son, as well as Daniyar Usenov, the former prime minister, over the deaths in last week's protests.
Moscow appears to have endorsed the interim government in Bishkek after Otunbayeva held her first official conversation as head of the government with Vladimir Putin, the Russian prime minister, on Thursday.
In one of her first public statements, Otunbayeva thanked Russia for its "significant support" in exposing what she termed the "nepotistic, criminal" government of Bakiyev.
On Wednesday, Robert Blake, the US assistant secretary of state for south and central Asian affairs, held talks with the interim leader in Bishkek.
"I feel optimistic about the steps [the interim government] is already taking ... the United States is prepared to help," he said after meeting Otunbayeva.
Otunbayeva meanwhile said that the future of the US use of the Kyrgyz Manas airbase, which is essential for supplies to its troops in Afghanistan, was not raised at the talks.
After last week's upheaval, members of Otunbayeva's government had suggested the lease of the base would be shortened.