WASHINGTON, March 3 -- U.S. and some European leaders on Tuesday conditioned the easing of sanctions against Russiaon a "full implementation" of peace deals over eastern Ukraine.

The agreement followed a video-conference meeting among U.S. President Barack Obamaand the leaders of Britain, France, Germany, Italy and the European Council.

"The leaders expressed their hope for the successful and complete implementation of the Minsk agreements and agreed that the easing of current sanctions would be linked to the full implementation of these agreements," the White Housesaid in a statement.

"They also affirmed their determination to act quickly and in unison to impose significant additional costs, if serious violations of the Minsk agreements occur or if Russian-backed separatists seek to gain new territory," said the statement.

Russian Foreign Minister Sergey Lavrov said on Monday in Geneva, where he met with U.S. Secretary of State John Kerry, that he welcomed "tangible progress" in the implementation of the cease-fire agreement reached in the Belarusian capital of Minsk on Feb. 12.

The top Russian envoy said "the cease-fire is being consolidated, heavy weapons are withdrawn," which are considered as central parts of the new peace deal. Past peace deals inked in Minsk in September last year were not fully executed.

Ukrainian President Petro Poroshenkotold European Council President Donald Tusk over the phone on Tuesday that the latest Minsk accord is not "fully" observed with "no comprehensive cease-fire and complete withdrawal of heavy armament" in place.

In their video-conference meeting, Obama and the European leaders called on all parties "to cease all military action, cooperate with the OSCE (Organization for Security and Cooperation in Europe) so that its monitors can verify a full pullback of heavy weapons, and complete the exchange of all prisoners."

The OSCE is serving as a mediator and observer of the implementation of the Minsk peace deals.

The leaders "emphasized their support for the OSCE and the need for its monitors to have full and unfettered access to the entire area of conflict, and they discussed ways to strengthen OSCE monitoring activities," the White House said.

Washington and its European allies have slapped rounds of sanctions on Russia over its annexation of Crimea and its alleged support for independence-seeking rebels in Ukraine's east, though Moscow has vehemently denied any involvement in the conflict there.

The number of people killed in eastern Ukraine since April last year has topped 6,000, despite repeated attempts for ceasefire, a UN spokesman said on Monday, citing the latest report from the Office of the UN High Commissioner for Human Rights.