Meanwhile, Obama is considering not attending the G8 Summit in Sochi, Russia, in June, if Russian troops remain in the Ukraine, a senior administration official familiar with the discussions told CNN.
Both officials spoke on condition of anonymity.
Kerry talks to Russian foreign minister
The Russian Foreign Ministry said maneuvers of armored vehicles from the Russian Black Sea Fleet in Crimea were needed for security and were in line with bilateral agreements.
U.S. Secretary of State John Kerry said he spoke with Russian Foreign Minister Sergey Lavrov on Friday morning about the airport and military activities, and Lavrov told Kerry that the Russians "are not engaging in any violation of the sovereignty" of Ukraine. Russia has a military base agreement with the country.
Lavrov told him the military exercises were prescheduled and unrelated to the events in Ukraine, Kerry said.
"I nevertheless made it clear that that could be misinterpreted at the moment,'' Kerry said, "and there are enough tensions that it is important for everybody to be extremely careful not to inflame the situation and send the wrong messages."
Yanukovych's news conference was under way in Russia, Kerry said, as he spoke with Lavrov.
Kerry said Lavrov had reaffirmed to him a commitment that Russia would "respect the territorial integrity of Ukraine."
"We would overwhelmingly stress today that we urge all parties -- all parties; that includes the new interim technical government, rightists, oppositionists and others, anybody in the street who is armed -- we urge all parties to avoid any steps that could be misinterpreted or lead to miscalculation or do anything other than to work to bring that peace and stability and peaceful transition within the governing process within Ukraine," Kerry said.
In a telephone call with European leaders, Russian President Vladimir Putin stressed the importance of avoiding a further escalation of violence in Ukraine, the Kremlin said in a prepared statement Friday.
Putin also called for a normalization of the situation, speaking with German Chancellor Angela Merkel, British Prime Minister David Cameron and European Council President Herman Van Rompuy, according to the Kremlin.
Crimea was handed to Ukraine by the Soviet Union in 1954. Just over half its population is ethnic Russian, while about a quarter are Ukrainians and a little more than 10% are Crimean Tatars, a predominantly Muslim group oppressed under former Soviet leader Josef Stalin.
Meanwhile, Russian lawmakers introduced two bills Friday to simplify annexing new territories into the Russian Federation and simplify access to Russian citizenship for Ukrainians, the state news agency Itar Tass said.
One bill also stipulates that the accession of a part of a foreign state to Russia should be taken through a referendum, according to Russian state news agency RIA Novosti.
Ukraine's President in Russia
Making his first public appearance since his ouster Saturday, Ukrainian President Viktor Yanukovych said the newly appointed interim government was not legitimate and did not represent the majority of Ukraine's 45 million citizens.
"I intend to continue the fight for the future of Ukraine against those who, with fear and with terror, are attempting to replace the power," Yanukovych said in Russian, not Ukrainian.
"Nobody has overthrown me. I was compelled to leave Ukraine due to a direct threat to my life and my nearest and dearest."