The G7 group of top economic powers today scrapped a planned meeting to be hosted by Russia as they sought to deepen Moscow's isolation over the Ukraine crisis.
After emergency talks on the Ukraine crisis called by US President Barack Obama, the G7 said they would hold a meeting in Brussels without Russia instead of the wider G8 summit that was to have taken place in Sochi.
The G7 also threatened tougher sanctions against Russia for its annexation of Crimea that has plunged relations between the West and Moscow to their lowest level since the end of the Cold War.
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"If our Western partners think that this format has outlived itself, then so be it," Lavrov told reporters.
"We are not trying to hold on to this format, and we see no great tragedy if it (the G8) does not meet," Lavrov said, insisting that Crimea has "a right to self determination."
Russia's takeover of the region was not "malicious intent," said Lavrov but was to "protect the Russians who have been living there for hundreds of years."
Kerry met with Lavrov for over an hour earlier in the day, his spokeswoman Marie Harf said, welcoming the Russia-Ukraine talks, the highest level contact between Russia and Ukraine since the start of the crisis.
He reiterated to Lavrov US concern about the massing of Russian troops on Ukraine's border and the treatment of Ukrainian troops, "including many Ukrainian service members who are missing," Harf said.
Kerry reminded Lavrov that Obama has signed an executive order "that provides the flexibility to sanction specific industries if Russia continues to take escalatory steps," Harf said, urging Russia to de-escalate the situation and pursue a dialogue with the Ukrainian government.
Ahead of the talks, Obama stressed that Europe and the United States were "united in our support of the Ukrainian government and the Ukrainian people" and "united in imposing a cost on Russia for its actions so far".
In Crimea, Russian forces stormed a Ukrainian navy ship, with an AFP correspondent reporting plumes of smoke as a Ukrainian defence spokesman said the crew had fired smoke grenades in self-defence.
Earlier today, the White House said it was "very concerned" about the risk of escalation as Russia massed its troops on Ukraine's eastern border.