Russian Foreign Minister Sergei Lavrov has spoken to U.S. Secretary of State John Kerry about the need to maintain a cease-fire in eastern Ukraine.
The Russian Foreign Ministry said Lavrov made the comments during a telephone conversation with Kerry on October 3.
Meanwhile, both pro-Russian separatists and the Ukrainian government claimed military gains October 3 in the battle for the airport in the rebel stronghold of Donetsk.
OSCE monitors in eastern Ukraine on October 3 reported intermittent "heavy shelling" in the northern part of Donetsk – where the government-controlled airport is located -- and scattered gunfire in other parts of eastern Ukraine.
Separatist fighters said they were in control of almost the entire airport, which includes an old terminal and a brand new one built at a cost of nearly $1 billion for the 2012 football European Championship.
The Ukrainian military confirmed that separatists had briefly seized the first floor of the old building but said they had since been pushed out, even though fighting continued.
Lavrov called for "strict compliance" with a cease-fire agreement signed on September 5 in Minsk, as well as an end to shelling in residential areas of Donetsk -- which are under the control of pro-Russian separatists.
Also on October 3, Russia's Foreign Ministry claimed the shell that killed a Swiss Red Cross worker in Donetsk on October 2 was fired from territory controlled by Ukrainian government forces.
In a statement, the ministry described the killing of Swiss aid worker Laurent DuPasquier as "murder."
"The fire came from positions taken by Ukrainian forces," ministry spokesman Aleksandr Lukashevich said in an accompanying video statement.
Despite increasing evidence that Russian military forces have been deployed in eastern Ukraine and are supporting the pro-Russian separatists there, Russia continues to deny that it has any forces on Ukrainian territory.
Russia's Foreign Ministry did not reveal how it had determined DuPasquier was killed by a shell fired from Ukrainian government-controlled territory.
Ukraine's government and the separatists have blamed each other for the death of the Swiss aid worker.
'Mass-Grave' Probe Demanded
In Geneva on October 3, Russian Duma speaker Sergei Naryshkin told the OSCE Parliamentary Assembly that Russia insisted an international tribunal investigate the alleged discovery of mass graves near Donetsk.
Russian media have reported that an "OSCE expert" confirmed the existence of two mass graves with more than 400 bodies in the area.
But the OSCE said on October 1 that the man making those claims, Latvian political activist Einars Graudins, was not a member of the OSCE monitoring mission and "has no link whatsoever" with the OSCE.
Graudins' mass-grave claims have not been independently confirmed.
Meanwhile, in Washington, a top U.S. official has accused Moscow of continuing to supply the pro-Russian separatists in eastern Ukraine with weapons -- despite the September 5 cease-fire deal.
State Department Assistant Secretary of State for European and Eurasian Affairs Victoria Nuland made those accusations on October 2.
With reporting by Interfax, ITAR-TASS, Reuters, and AP