Ukraine's new acting government is not legitimate, Russian prime minister Dmitry Medvedev has said. "If people crossing Kiev in black masks and Kalashnikov rifles are considered a government, it will be difficult for us to work with such a government," the prime minister said.

"Some of our foreign, western partners think otherwise, considering them to be legitimate authorities. I do not know which constitution, which laws, they were reading, but it seems to me it is an aberration of perception when something that is essentially the result of a mutiny is called legitimate."

He also called the legitimacy of many of Ukraine's governing bodies "doubtful", adding: "There is no one to deal with there [in Ukraine]; masked and armed people are no partners for dialogue."

The Russian PM said he did not understand what was happening in Ukraine. "There is a real threat to our interests and to the lives of our citizens," he said. "There are big doubts about the legitimacy of a whole series of organs of power that are now functioning there."

But Medvedev also said any legally-binding Russian-Ukrainian agreements "must be honoured". There are fears about the future of a gas deal agreed in December under which Russia reduced the gas price for Kiev to $268.50 per 1,000 cubic metres, from the $400 which Ukraine had paid since 2009.

"Those agreements which are legally binding must be honoured," Medvedev said. "We are not cooperating with personalities or isolated individuals. These are inter-state relations. We are neighbours, close nations, and we cannot run away from one another. Whatever has been signed must be honoured. For us, Ukraine remains a serious and important partner."

Vladimir Putin, Russia's president, has yet to comment on the events that swept Ukrainian president Viktor Yanukovych out of power on Saturday.

The hunt is now on for Yanukovych, who is currently believed to be hiding in the pro-Russian Crimean peninsula. The country's new acting government has issued a warrant for his arrest, accusing him of the mass murder of protesters who died in street clashes last week.

Ukraine's acting interior minister, Arsen Avakhov, said on his official Facebook page on Monday that a warrant had been issued for the arrest of Yanukovych and several other officials for the "mass killing of civilians". At least 82 people, primarily protesters, were killed in clashes in the capital, Kiev, last week.

After signing an agreement with the opposition, Yanukovych fled the capital for eastern Ukraine. Avakhov said he tried to fly out of Donetsk but was stopped, then went to Crimea. Yanukovych appeared in a video address on Saturday evening claiming he was still the president, but he has lost the support of most of his party and his main goal now will probably be to flee the country without being arrested.

Avakhov said Yanukovych arrived in Crimea on Sunday, relinquished his official security detail and then drove off to an unknown location. There were rumours that a yacht named the Bandido, believed to belong to Yanukovych's son, was spotted in the harbour in the Crimean port of Balaclava.

In Balaclava on Monday there was no sign of either the yacht or the president, and locals claimed they had not seen Yanukovych in recent days. Officials in Sevastopol also professed ignorance. In Kiev, western diplomats said they had no idea of the president's location.

Calls are mounting in Ukraine to put Yanukovych on trial after a tumultuous presidency in which he amassed powers, enriched his allies and cracked down on demonstrators. Anger boiled over last week after snipers attacked protesters in the bloodiest violence in Ukraine's post-Soviet history.

The turmoil has raised fears that the country, with a population of 46 million, could split apart. The economy is on the brink of default and loyalties are torn between Europe and Russia.

Tensions have been mounting in Crimea, where pro-Russian protesters raised a Russian flag on a city hall in one town and scuffled with police. Russia maintains a big naval base in Sevastopol that has complicated relations between the countries for two decades.

The protests were sparked in November when Yanukovych shelved an agreement with the EU and turned towards Russia. The movement quickly expanded its grievances to alleged corruption and human rights abuses, and called for Yanukovych's resignation.

"We must find Yanukovych and put him on trial," said Leonid Shovtak, a 50-year-old farmer from the western Ivano-Frankivsk region who came to Kiev's Independence Square to take part in the three-month protest movement. "All the criminals with him should be in prison."

The parliamentary speaker assumed the president's powers on Sunday, even though a presidential aide told the Associated Press on Sunday that Yanukovych planned to stay in power.

The speaker, Oleksandr Turchinov, said top priorities included saving the economy and "returning to the path of European integration", according to news agencies. The latter phrase is certain to displease Moscow, which wants Ukraine to be part of a customs union that would rival the EU and bolster Russia's influence. Russia granted Ukraine a $15bn (£9bn) bailout after Yanukovych backed away from the EU deal.

The US ambassador Geoffrey Pyatt said America was ready to help Ukraine get aid from the International Monetary Fund. The EU is reviving efforts to strike a deal with Ukraine that could involve billions of euros in economic perks. The EU foreign policy chief, Lady Ashton, is visiting Kiev on Monday and Tuesday.

The protest movement has been in large part a fight for the country's economic future – for better jobs and prosperity. Ukraine has struggled with corruption, bad government and short-sighted reliance on cheap gas from Russia. Political unrest has worsened the deficit and caused volatile exchange rates, and may have pushed the economy back into a recession.

Per capita economic output is only around $7,300, even adjusted for the lower cost of living, compared with $22,200 in Poland and around $51,700 in the US. Ukraine ranks 137th in the world for output, behind El Salvador, Namibia, and Guyana.