In recent weeks, pro-Russia demonstrators in eastern Ukraine have seized government buildings and engaged in clashes with supporters of the Ukrainian government.
Violence erupted late Thursday in the city of Donetsk, where people rallying in support of the central authorities were attacked by pro-Russia crowds.
At least one person died and 17 others were wounded, according to the local health department.
On Thursday, Putin did not sound conciliatory about Ukraine when he convened a meeting of his Security Council, an advisory body of top defense and security officials, including Lavrov.
"It's foremost Ukraine's internal crisis," Putin said. "But, regrettably, we have been drawn into these events."
"We can't ignore the developments around Ukraine, Crimea and everything related to that uneasy problem, which, I want to underline, has emerged through no fault of ours," he said.
In brief remarks at the start of the session, Putin didn't refer to harsh warnings from President Barack Obama and other Western leaders not to annex Crimea.
Merkel said the European Union and other Western nations would soon freeze bank accounts of Russians and implement travel restrictions, if Moscow refuses to enter "negotiations that achieve results."
"Let me be absolutely clear so that there is no misunderstanding, the territorial integrity of Ukraine is not up for discussion," she said.
If Moscow does not begin to "de-escalate" the situation, Merkel said, the 28 European Union nations, the US and other allies are prepared to take even stronger measures that would hit Russia economically.
"If Russia continues on its course of the past weeks, that will not only be a great catastrophe for Ukraine," Merkel said in the nationally televised address. "It will cause massive damage to Russia, both economically and politically."
