MOSCOW, Oct 29 (Reuters) - Russia's lower house of parliament is ready to cooperate with the new assembly in Ukraine, its chairman said on Wednesday, although it will be dominated by pro-Western forces.

Parties that want to move Kiev further away from Moscow's orbit towards mainstream Europe will lead the Verkhovna Rada after an election on Sunday, held despite fighting between government forces and pro-Russian separatists in east Ukraine.

"We hope that the newly elected Verkhovna Rada will make its contribution to ending the civil war, resolving the crisis and de-escalating tensions," Russian news agencies Sergei Naryshkin, the speaker of the State Duma lower house, as saying.

"Duma lawmakers are ready for any contacts, for the restoration of normal inter-parliamentary relations."

Foreign Minister Sergei Lavrov has said Moscow will recognise the outcome of the election even though voting did not take place in rebel-held areas in the east and forces traditionally loyal to Moscow performed poorly.

The head of the international affairs committee in the Federation Council, the upper house, was quoted by Russian media as saying his chamber would also cooperate with the Ukrainian parliament although he said it was hard to see how this would work out in practice.

Russia and Ukraine blame each other for the conflict in eastern Ukraine, in which more than 3,700 people have been killed since mid-April.

(Reporting by Katya Golubkova, Editing by Timothy Heritage)