Pro-Ukrainian activists have been beaten up by pro-Russian groups at a rally in Crimea’s city of Sevastopol.
The activists were attacked with whips, a BBC reporter at the scene says, describing the scenes as very ugly.
Russian troops and allied militias are now in de-facto control of Ukraine’s autonomous region ahead of a referendum, which Kiev says is illegal.
The US has warned Moscow that any moves to annex Crimea, an autonomous region, would close the door to diplomacy.
The violence erupted when pro-Russian groups attacked dozens of people guarding a rally to commemorate the 200th anniversary of Ukrainian poet and national hero Taras Shevchenko.
The crowd threw missiles at a car as the activists tried to flee the scene, smashing windows.
Some of the attackers were Russian Cossacks.
The rally was attended by about 200 people.
A rival pro-Russian demonstration was also staged in the city – the base of Russia’s Black Sea Fleet.
The exchange between Kerry and Lavrov came in a telephone conversation on Saturday, a US state department official said.
“He [John Kerry] made clear that continued military escalation and provocation in Crimea or elsewhere in Ukraine, along with steps to annex Crimea to Russia would close any available space for diplomacy, and he urged utmost restraint,” the official said.
Lavrov had earlier said that the crisis in Ukraine was “created artificially for purely geopolitical reasons”.
Russian President Vladimir Putin has insisted he has the right to protect Russian interests and the rights of ethnic Russians in Crimea.
Moscow has been tightening its military grip on the Crimean peninsula.
The pro-Russian authorities there have called the March 16 referendum to vote on whether to secede from Ukraine and join Russia.
Ukraine and the leading Western nations have called the planned vote illegitimate.
Unrest in Ukraine erupted in November, following former President Viktor Yanukovych’s last-minute rejection of a landmark EU deal in favour of a bailout from Russia.
Yanukovych was ousted last month, and a new government has been voted in by the Ukrainian parliament.
Presidential elections are scheduled for May 25.