Viktor Yanukovych has vowed to fight for Ukraine, in his first public appearance since being ousted as president last week.
Speaking in Russia, he said he was “not overthrown” but was compelled to leave Ukraine after threats to his life.
In the latest flare-up, Ukraine accused Russian troops of seizing two airports in Crimea – charges denied by Moscow.
Russian President Vladimir Putin has called for a rapid return to normality in Ukraine.
Mr Putin spoke to Western leaders to emphasise “the extreme importance of not allowing a further escalation of violence”, the Kremlin said.
n other developments:
“I intend to continue to struggle for the future of Ukraine, against terror and fear,” Mr Yanukovych told the news conference in the Russian city of Rostov-on-Don.
“I can’t find words to characterise this new authority. These are people who advocate violence – the Ukrainian parliament is illegitimate.
“What’s going on now is lawlessness, lack of authority, and terror. Decisions in parliament were taken under duress.”
He apologised to the Ukrainian people for not having “enough strength to keep stability” and described his usurpers as “young, neo-fascists”.
He insisted he did not “flee anywhere”, explaining that his car was shot at as he left Kiev for the north-east city of Kharkiv and he was forced to move around Ukraine amid fears for the safety of himself and his family.
He said he arrived in Russia “thanks to a patriotically-minded young officer” and was given refuge in Rostov, near the Ukrainian border, by an old friend.
Speaking in Russian, Mr Yanukovych said he would return to Ukraine “as soon as there are guarantees for my security and that of my family”.
But he ruled out taking part in elections planned for 25 May, describing them as “illegal”.
And he made clear his view that the only way out of the crisis is to implement an EU-backed compromise agreement he signed with opposition leaders last week before he was deposed.
He said the current turmoil in Crimea was “an absolutely natural reaction to the bandit coup that occurred in Kiev” and added that he was surprised by the restraint shown by Russian President Vladimir Putin so far.
But he also stressed that “military action in this situation is unacceptable” and said he wanted Crimea to remain part of Ukraine.
Earlier, Ukraine’s general prosecutor said he would ask Russia to extradite Mr Yanukovych on suspicion of mass murder following the deaths of more than 80 people in last week’s violent clashes between protesters and the police.
Armed men took over Sevastopol and Simferopol airports in the early hours of Friday.
Acting national security chief Andriy Parubiy said the airports were back in the control of the Ukrainian authorities, but the men were now manning checkpoints on the surrounding roads.