"The West wants — and this is how it all began — to seize control of Ukraine because of their own political ambitions, not in the interests of the Ukrainian people," Lavrov said on Friday.
U.S. President Barack Obama, speaking to reporters in Seoul, South Korea, said he will call key European leaders later Friday to discuss what's happened since a deal was reached last week in Geneva to de-escalate the crisis.
Russia and Ukraine had reached an agreement calling on all parties in the country to lay down arms and vacate public buildings. Pro-Russian militia have been occupying government buildings in more than 10 cities in eastern Ukraine while the nationalist Right Sector movement is still in control of two public buildings in Kyiv.
There were scattered reports of violence Friday. Ukraine's Defence Ministry said a grenade fired from a launcher caused an explosion in a helicopter at an airfield outside the eastern city of Kramatorsk. Deputy Minister Vasyl Krutov said the pilot was injured.
In southeastern Ukraine, seven people were injured by a blast at a checkpoint set up by local authorities and pro-Ukraine activists outside the Black Sea port of Odesa. Local police spokesman Volodymyr Shablienko said unknown men had thrown a grenade at the checkpoint.
The West has accused Russia of fueling the unrest in Ukraine's east and failing to use its influence on the pro-Russian insurgents.
"For seven days, Russia has refused to take a single concrete step in the right direction," U.S Secretary of State John Kerry said Thursday.
"Not a single Russian official, not one, has publicly gone on television in Ukraine and called on the separatists to support the Geneva agreement, to support the stand-down, to give up their weapons, and get out of the Ukrainian buildings," Kerry said.
Lavrov said on Friday the militia in the east "will be ready" to lay down arms and vacate the buildings "only if Kyiv authorities get down to implementing the Geneva accords, clear out that shameful Maidan and liberate the buildings that have been illegally seized."
Moscow in March recognized a hastily called referendum in Ukraine's Black Sea peninsula of Crimea and annexed it weeks later, attracting condemnation of the West as well as sanctions targeting individuals. Kerry said that unless Moscow took immediate steps to relax tensions, Washington would impose additional sanctions.
Russia's economy is already hurting from its involvement in Ukraine.
The Standard & Poor's credit agency on Friday cut Russia's credit rating for the first time in more than five years. The main concerns cited by the agency were the flight of capital and the risk to investment in Russia since the Ukraine crisis blew up late last year.
Credit ratings are important for the economy because they determine the cost of borrowing on international markets. Russian Economic Development Minister Alexei Ulyukayev sought to play down the downgrade, calling it "partly politically motivated."
Russia announced new military exercises Thursday involving ground and air forces near its border with Ukraine, swiftly responding to a Ukrainian operation to drive pro-Russia insurgents out of occupied buildings in the east. At least two people were killed in a clash at a checkpoint.
Yuras Karmanau in Donetsk and Julie Pace in Seoul contributed to this report.