Russian news agencies quoted a statement by Yanukovich as saying he had asked Moscow to guarantee his personal safety.
The statement could not be independently verified and it was not clear where Yanukovich was, although some media groups have suggested he is in Moscow after fleeing Ukraine, where he was toppled by opposition forces at the weekend.
Russian President Vladimir Putin's spokesman said he had no information and could not comment on the statement.
"I, Viktor Fedorovich Yanukovich appeal to the people of Ukraine. As before I still consider myself to be the lawful head of the Ukrainian state, chosen freely by the will of the Ukrainian people," he was quoted as saying.
"Now it is becoming clear that the people in southeastern Ukraine and in Crimea do not accept the power vacuum and complete lawlessness in the country, when the heads of ministries are appointed by the mob."
"On the streets of many cities of our country there is an orgy of extremism," he said, adding that he and his closest aides had been threatened physically.
"I have to ask the Russian authorities to provide me with personal safety from the actions of extremists."
Russian television showed what it said was a copy of the statement.
Interfax news agency quoted a source in the authorities as saying Moscow would ensure Yanukovich's safety on the Russian territory.
"In connection with the appeal by president Yanukovich for his personal security to be guaranteed, I report that the request has been granted on the territory of the Russian Federation," the source was quoted as saying.
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