"I am the legitimate president of Ukraine, elected by the people of Ukraine, and was elected in a free and democratic vote," he declared.
Speaking to reporters in Rostov-on-Don in southern Russia, he said he has not met with Russian President Vladimir Putin, but said Moscow "cannot stay indifferent" to events in Ukraine.
He said Russia should "use all the leverage it has to prevent the chaos, the terror, that is unfolding in Ukraine" but added, "I do not accept any attempts for an intervention to break the sovereignty and integrity of Ukrainian territory."
Yanukovych's remarks come against the backdrop of new tensions in Ukraine, including the takeover of an airport near Sevastopol in Ukraine Friday by unidentified armed men who may belong to the Russian military.
On other points:
• He denied that he ordered police to open fire on protesters in Kiev during massive demonstrations that left more than 80 people dead.
• He said he would not take part in May presidential elections that were set up under a Feb. 21 agreement reached between he, opposition leaders and the foreign ministers of France, Poland,Germany and Russia.
• He vowed "to keep on fighting for Ukraine's future" against new Ukrainian authorities that he described as "illegitimate."
Asked why he left Kiev for eastern Ukraine and eventually Russia after the agreement was announced, Yanukovych said he feared for his life and that his car had been "shot at from all sides."
"Nobody overthrew me, I was forced to leave Ukraine under the immediate threat to my life and the life of my family," he told reporters.
At one point he apologized for the unrest in Ukraine, saying "I didn't have the power and strength to maintain stability and to prevent it from happening."
He called for all sides to implement an agreement signed by him and the foreign ministers of France, Poland, Germany and Russia that that would set up new elections.
Parts of the agreement were been largely surpassed after Ukraine's parliament stripped Yanukovych of his presidency and elected an interim leader and new cabinet.
While Yanukovych spoke in southern Russia, tensions mounted in Ukraine's Crimea region with the takeover of the airport near Sevastopol by pro-Russian groups.
Ukraine's State Border Guard also reported that a coast guard base had been surrounded by about 30 Russian marines, the Associated Press reports.
Ukraine's interior minister called the move an "armed invasion."
"I can only describe this as a military invasion and occupation," Ukraine's new Interior Minister Arsen Avakov wrote in a post on Facebook.
The Russian foreign ministry refused to comment to the Associated Press, but Russia's defense ministry told the Interfax news agency that there had been "no provocative acts in relation to units and divisions" from Russian forces stationed in the region.
Dozens of armed men in military uniforms without markings have also apparently taken over the main airport in Simferopol, the capital of Crimea, although it has not been confirmed that the men at either airport belong to Russian military units.
There were also reports that some of the men have started to partially withdraw.
While no violence has so far been reported, any Russian military incursion in Crimea would dramatically raise the stakes in Ukraine's conflict, which saw the pro-Russian president flee last weekend after three months of anti-government protests.
Moscow has vowed to protect Russian-speaking Ukrainians in Crimea, where it has a major naval base, and Ukraine and the West have warned Russia to stay away.
"There is an acute need right now to support our families, make them secure, and protect our society," said Andrey Sitnikov in Sevastopol, who says he is there as private citizen.
At Sevastopol's Belbek International Airport on Friday, around 15 to 20 members of a Ukrainian political party called the Russian Bloc representing ethnic Russians set up an informal blockade to support the armed men with their own civilian barricade a hundred meters from the airport.
A private car has coffee, tea and sandwiches in its open trunk, free for anyone to take.
A Russian truck with insignias and number plates removed was spotted exiting the Sevastopol airport.
More checkpoints have been set up in the strongly pro-Russian city scrutinizing all arrivals and Reuters reported that Russian military helicopters have traveled to the Crimea.
The blockade may signal an unwillingness to negotiate with Kiev, said Yaroslav Pylynskyi, director of the Kennan Institute at the Wilson Center, a policy research institute in Kiev.
"I heard the people blocking the airport were trying to prevent people from Kiev coming for negotiations," he said.
"The [ethnic Russians in Crimea] did not want negotiations, because they are being controlled by Moscow. I guess they also do not know what to do in that situation."
Responding to the situation on Friday, Ukrainian lawmakers asked the the United Nations' Security Council to address the country's political turmoil.
On Thursday, armed men seized the Crimea parliament as Russian jets streaked near the border and a newly created Ukraine government formed to try to end a crisis that threatens to split the country following the ouster of its president.
After capturing the parliament and government offices in Simferopol the masked men raised the Russian flag over the parliament building.
Authorities in Switzerland and Austria moved to freeze any funds belonging to the former leader or his family and allies.
In a separate development Friday, the National Bank of Ukraine — the nation's central bank — put a $1,500 limit on foreign currency withdrawals in a bid to counter falling values in the hryvnia, Ukraine's currency.