Oleksandr Turchynov, who stepped in as president after Yanukovych fled Kiev last weekend, urged Russian President Vladimir Putin to stop "provocations" in Crimea and pull back military forces from the peninsula. Turchynov said the Ukrainian military would fulfill its duty but would not be drawn into provocations.
In Kiev, Ukraine's newly named interior minister accused Russia of military aggression.
"I can only describe this as a military invasion and occupation," Arsen Avakov wrote in a Facebook post.
In recent conversations between U.S. and Russian officials, including a lengthy telephone conversation between Obama and Putin just last week, Obama said the U.S. has made clear that Russia can be part of an international community's effort to support the stability and success of Ukraine.
But, he said Friday, "we are now deeply concerned by reports of military movements taken by the Russian Federation inside of Ukraine."
Earlier Friday, as pro-Russia gunmen patrolled Crimean streets in armored vehicles and took over airports there, Secretary of State John Kerry warned Moscow against military moves in Crimea that could further inflame tensions.
Kerry and White House spokesman Jay Carney both said any Russian military intervention would be a grave mistake and that the United States was watching closely. They did not spell out any consequences for an intervention.
U.S. Ambassador to the U.N. Samantha Power told reporters that the United States was proposing an urgent mediation mission to help resolve Ukraine's crisis.
The Russian armored personnel vehicles seen by AP reporters were parked on the side of the road near the town of Bakhchisarai, apparently because one of them had mechanical problems.
Russia is supposed to notify Ukraine of any troop movements outside the Black Sea Fleet naval base it maintains in Sevastopol under a lease agreement with Ukraine.
The Russian Foreign Ministry said the military vehicles were deployed to ensure the security of its base and didn't contradict the lease terms.
A duty officer at the Ukrainian Defense Ministry said it had no information about the vehicles' movements.
AP journalists approaching the Sevastopol airport found the road leading to it blocked by two military trucks and a handful of gunmen wearing camouflage uniforms and carrying assault rifles.
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.
Meanwhile, Ukraine International Airlines said it had canceled flights to and from the Simferopol airport on Friday evening and Saturday because of the closure of the airspace over Crimea. The announcement did not say who had ordered the closure.
At the airport, dozens of armed men in military uniforms without markings patrolled the area. 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-defense unit ensuring that no "radicals and fascists" arrive from other parts of Ukraine. There was no way to verify his account.
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 Friday.