Europe's main elections monitoring group said on Tuesday it hoped to be able to oversee Russia's presidential vote next year despite its criticism of the conduct of last weekend's parliamentary election.

Moscow's relations with the OSCE's vote monitoring arm, the Office of Democratic Institutions and Human Rights (ODIHR), have been fraught since the group refused to send observers to the 2007 parliament polls, citing obstructions by authorities.

My strong hope that it would not be long before we receive an invitation to observe Russia's presidential elections, Janez Lenarcic, ODIHR's director, told a news conference on the sidelines of an OSCE ministerial meeting in the Lithuanian capital.

Russia's presidential election is due in March next year.

The observers said after the Sunday election for Russia's lower house of parliament, the State Duma, that they had seen some ballot stuffing and that the vote was unfairly slanted in favour of Prime Minister Vladimir Putin's ruling party.

Russia's Central Election Commission said Putin's United Russia party was set to have 238 deputies in the 450-seat Duma, down from 315 seats in the outgoing lower house.

The result was Putin's worst election setback since he came to power 12 years ago and signalled growing weariness with his domination of Russian politics as he prepares to reclaim the presidency in the March election.

Lenarcic repeated criticisms of the Duma election, saying it had serious shortcomings in regard of favouring one party.

The OSCE was formed during the Cold War in part as a way for the Western and Soviet blocs to discuss human rights.

The Office for Democratic Institutions and Human Rights (ODIHR) is the OSCE's specialized institution which deals with elections, human rights, and democratisation.

(Reporting by Nerijus Adomaits and Aleks Tapinsh Editing by Maria Golovnina)