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."
In his hourlong news conference, Yanukovych accused the interim authorities in Ukraine of propagating violence. He spoke against a backdrop of Ukraine's blue-and-yellow flags before reporters in the Russian city of Rostov-on-Don about 700 miles south of Moscow.
"I never gave any orders to shoot," he said, adding that he sought peace and that the security forces took up arms only when their lives were at risk.
Yanukovych is wanted in Ukraine on charges connected to the deaths of demonstrators, who were protesting his decision to scrap a European Union trade deal in favor of one with Russia.
Armed men at airports
Back in Kiev, Andrii Parubii, chief of national security and defense, said Ukrainian military and police forces had stopped Russian military forces from seizing two airports in the Crimean region.
The Russian military is on the outside of both airports, Parubii said in a televised news conference from the Ukrainian parliament.
Weapons were not used during the operation, according to Avakov, the interior minister.
Russian armored vehicles were moving toward Simferopol, the regional capital, on Friday, the Ukrainian news outlet TSN reported.
Men in military uniforms had been seen patrolling the airport in Simferopol, as well as a military and civilian airbase in nearby Sevastopol since early Friday.
Avakov said the armed men at the Sevastopol air base were troops from Russia's Black Sea Fleet, stationed in the port city. They were in camouflage uniforms without military insignia, he said.