MOSCOW (Reuters) - Russian Foreign Minister Sergei Lavrov and U.S. Secretary of State John Kerry agreed in a phone conversation on Sunday on the importance of ensuring a swift ceasefire in eastern Ukraine, a Foreign Ministry statement in Moscow said.

But the State Department said Kerry did not accept Lavrov's denial that heavy weapons from Russia were contributing to the conflict and urged him "to stop the flow of heavy weapons and rocket and artillery fire from Russia into Ukraine, and to begin to contribute to deescalating the conflict."

The Russian statement described the crisis in Ukraine as an "internal conflict."

Washington and the West accuse Moscow of supporting rebels fighting Ukrainian troops in the east of the former Soviet republic. Moscow denies involvement.

(Reporting by Gabriela Baczynska; Editing by Lidia Kelly)