The US says Russia has failed to live up to an agreement to end the crisis struck in Geneva last week.
American officials say Russia is behind unrest in eastern Ukrainian cities.
Ukraine has warned it will consider any crossing into its territory by Russian troops stationed on the border as a "military invasion".
"We do not accept false declarations about humanitarian action," the chief of staff of acting President Olexander Turchynov told the Interfax-Ukraine news agency.
"We will destroy the attackers."
In a separate development, Russia's foreign currency ratings have been cut by the credit ratings agency Standard & Poor to one notch above "junk" status.
The agency warned that further downgrades were possible if the West imposed tighter sanctions against Moscow.
'Bloody crime'Pro-Russian separatists have been occupying key buildings in a dozen eastern Ukrainian towns, defying the central government.
A bride passes by masked pro-Russian activist near a barricade outside a government building in the eastern city of Donetsk Pro-Russian separatists are refurbishing old rifles at a makeshift camp in the town of SlovianskUkraine has launched military raids to regain the buildings, which Mr Lavrov described as a "bloody crime".
"The West... wants to seize Ukraine so to speak, being solely motivated by its own geopolitical ambitions and not the interests of the Ukrainian people," Mr Lavrov said, according to AFP.
"The might of US propaganda" was aimed "at smearing Russia, smearing those who protest against the illegal actions of the [Kiev] authorities," he went on.
In response to Mr Lavrov's comments, Ukrainian Prime Minister Arseniy Yatsenyuk said Russia wanted to "start World War Three" by occupying Ukraine "militarily and politically" and by creating a conflict that would spread to the rest of Europe.
Natalia Antelava investigates who entered Mariupol's city council buildingRussia has ordered new military exercises on its border following the Ukrainian military raids, drawing condemnation from Kiev.
Moscow has tens of thousands of troops along its side of the border and on Friday acting Ukrainian Defence Minister Mikhail Koval said they had come within a kilometre of the border.
On Thursday morning raids by Ukrainian commandos on pro-Russian checkpoints around the town of Sloviansk left at least two separatists dead.
There have also been reports from the port city of Odessa indicating that an explosion at a checkpoint injured at least seven people.
Russia 'fantasy'US President Barack Obama said he would talk to some key European leaders on Friday evening to make sure they shared his "assessment in terms of what has happened since the Geneva talks" held on 17 April.
Continue reading the main story Steve Rosenberg BBC News, DonetskThese are strong words from John Kerry. But they're unlikely to convince the Kremlin to change its position on Ukraine.
Experience shows that President Putin doesn't respond well to Western criticism. He believes the United States and the EU are hypocritical, that the West is the sponsor of what Moscow sees as an illegitimate government in Kiev. He suspects Western governments are plotting to undermine Russia's national interests.
If you analyse the tough language coming out of Moscow in recent days and look at the way this conflict is being portrayed by Russian TV channels - as Kiev sending in troops against innocent civilians - there is no sign that the Kremlin is prepared to change its view.
If that is the case, then Russian military intervention in eastern Ukraine on the pretext of protecting Russians and Russian-speakers there remains a distinct possibility.
On Thursday US Secretary of State John Kerry issued a strongly worded statement, in which he called on Moscow to help defuse the crisis or face further sanctions.Mr Kerry praised the interim authorities in Kiev, saying they had honoured the agreement struck in Geneva to de-escalate the crisis.
But he said Russia had "put its faith in distraction, deception and destabilisation" and said it had failed to call for separatists to leave official buildings and give up their arms as stipulated by the Geneva agreement.
He also accused Russian media of promoting President Vladimir Putin's "fantasy" about events in Ukraine.
Mr Kerry said US intelligence was confident that Russia was "playing an active role in destabilising eastern Ukraine" with personnel, weapons, money and operational planning".
Unrest began in Ukraine last November over whether the country should look towards Moscow or the West.
Last month, Russia annexed Ukraine's mainly ethnic-Russian Crimea. This followed a referendum in the region that backed joining the Russian Federation but which the West and Kiev deemed illegal.
Are you in eastern Ukraine? How has the unrest affected you? You can email us your experiences at haveyoursay@bbc.co.uk, using the subject line 'Ukraine'.