Medvedev's statement followed the issuance of a "mass killings" arrest warrant for ousted Ukrainian President Viktor Yanukovych, who has vanished in eastern Ukraine.
"Strictly speaking, there is no one to talk to, there. There are big doubts about the legitimacy of a whole series of organs of power that are now functioning there. ... It is an aberration to call legitimate what is essentially the result of an armed mutiny," Medvedev said.
Russian Foreign Minister Sergei Lavrov, has maintained opposition leaders "seized power" illegally and Moscow recalled its ambassador to Kiev, the Times said.
Maintaining a high-level dialogue on developments in Ukraine, Lavrov has spoken by telephone with U.S. Secretary of State John Kerry, who has voiced support actions taken by Ukraine's lawmakers.
Acting Interior Minister Arsen Avakov, now Ukraine's top law enforcement official, said Monday on his Facebook page an arrest warrant has been issued for Yanukovych and "other [former] government officials," the Kiev Post reported.
The warrant for "mass killings of civilians" did not spell out which killings, but the Post said it was presumed the investigation centers on whether Yanukovych hired snipers or ordered riot police to shoot demonstrators in January and February.
Nearly 100 civilians have been killed in the demonstrations, including at least 75 people last week, triggering Yanukovych's flight from Kiev and eventual impeachment Saturday.
In Kiev, the barricades around Independence Square remained in place Monday, but the lines of riot police were gone.
Avakov said authorities lost Yanukovych early Monday near his residence in the Balaklava district of Crimea where he released his guards from duty.
Yanukovych's whereabouts are currently unknown, the British newspaper the Daily Telegraph noted Monday.
Avakov said a criminal case also was opened against Yevhen Zhylyn, leader of Oplot, a pro-government militant group in Kharkiv. The organization gained notoriety when it released a video on YouTube featuring Zhylyn saying the group cut the ear of a demonstrator and telling people to "get ready for bloodshed."
Oleksandr Yefremov, head of Yanukovych's Party of Regions, announced Monday the party would join the opposition to the new interim government formed and led by acting president Oleksandr Turchynov, the Post said
"The Party of Regions faction members had a meeting. Since you've taken over power and you have all the chances to form new coalition government, we decided to go into the opposition," Yefremov said. "We took a decision that we are going in opposition."
Ukrainian Democratic Alliance for Reforms party head Vitali Klitschko said "people are waiting for justice and lustration of authorities." Among the some of the steps he proposed were releasing remaining political prisoners, independent investigations into the accusations of criminal activities of Yanukovych's regime and his allies, and investigations into judges who persecuted activists.
Appointing a new Central Election Commission quickly was crucial to efforts to conduct a presidential election May 24, Klitschko said.
Opposition leader Julia Tymoshenko, 53, freed from prison during the culmination of the weekend's demonstrations, accepted an offer from German Chancellor Angela Merkel to obtain treatment at a Berlin hospital, Tymoshenko's website said Monday. She suffered a spinal disc herniation and participated in several hunger strikes after she was sentenced and imprisoned in 2011 on embezzlement and abuse of power charges.