Russia denied "violation of sovereignty" said US Secretary of State John Kerry, but any Russian military incursion in Crimea would dramatically raise the stakes in the conflict.
Pro-Russian President Viktor Yanukovych fled Ukraine last weekend after three months of anti-government protests.
Speaking in Russia yesterday he vowed to "keep fighting for the future of Ukraine," though he called any military action "unacceptable".
Moscow has pledged 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.
The move came as Yanukovych made his first public appearance since fleeing Ukraine in the southern Russian city of Rostov-on-Don, not far from the Ukrainian border. It was the first confirmation that he had left the country, and he said he was "forced" to do so only after his family received threats.
"I intend to keep fighting for the future of Ukraine," he said.
Yanukovych said he supports Crimea's residents who are worried about "nationalists" in Kiev and added that Russia cannot stand by while events in Ukraine unfold.
But he added: "Any military action in this situation is unacceptable."
The prosecutor-general's office in Kiev said it would seek Yanu-kovych's extradition to Ukraine, where he is wanted on suspicion of mass murder in last week's clashes between protesters and police, when more than 80 people died.
Also in Kiev, Ukraine's parliament adopted a resolution demanding that Russia halt steps it says are aimed against Ukraine's sovereignty and territorial integrity, and called for a UN Security Council meeting on the crisis. Ukraine's new interior minister, Arsen Avakov, wrote on Facebook: "I can only describe this as a military invasion and occupation."
The chief of Ukraine's security council, Andriy Parubiy, seemed to strike a less strident tone later, saying gunmen had tried to "seize" the airports in the Crimean cities of Simferopol and Sevastopol, but insisting that "de-facto the airports are controlled by the law enforcement bodies of Ukraine."
Ukraine's State Border Guard Service also said about 30 Russian marines from Russia's Black Sea Fleet, based in Sevastopol, had taken up position outside the Ukrainian Coast Guard base in the area. It said the marines said they were there to prevent any weapons at the base from being seized by extremists.
Journalists approaching the Sevastopol airport found the road leading up to it blocked by two military trucks and gunmen wearing camouflage uniforms.
A car with Russian military plates was stopped at the roadblock. A man wearing a military uniform with a Russian flag on his sleeve got out of the car and was allowed to enter on foot after a brief discussion with the gunmen.
At the airport serving Simferopol, commercial flights were landing and taking off despite dozens of armed men in military uniforms without markings patrolling with assault rifles. They didn't stop or search people leaving or entering the airport, and refused to talk to journalists.
One man who identified himself only as Vladimir said the men were part of the Crimean People's Brigade, which he described as a self-defence unit ensuring that no "radicals and fascists" arrive from other parts of Ukraine.
The airport deployments came a day after masked gunmen with rocket-propelled grenades and sniper rifles seized the parliament and government offices in Simferopol and raised the Russian flag. Ukrainian police cordoned off the area but didn't confront the gunmen. They remained in control of the buildings yesterday.
Russia's state RIA Novosti and Interfax agencies said Russian servicemen stationed in Crimea have not moved into the airports.
Speaking in Colombia, US Secretary of State John Kerry said he had raised the issue of reports of Russian armoured vehicles in Ukraine with Russian Foreign Minister Sergei Lavrov.
He said: "While we were told that they are not engaging in any violation of the sovereignty and do not intend to, I made it clear that it is important for everybody to be extremely careful not to send the wrong messages."