Russia on Monday said the expected election of Bronislaw Komorowski as Poland's president offered an opportunity to boost relations, DPA reported.
"Hopefully, Komorowski will help make the policy of closer relations between Moscow and Warsaw irreversible," said Sergei Mironov, chairman of Russia's Federation Council.
Relations between the two countries have been troubled because of political and historic differences, including the issue of the murder of some 22,000 Polish soldiers and civilians by Soviet secret forces at Katyn in 1940.
Komorowski, of the centre-right Civic Platform party, is tipped to win Sunday's election against Jaroslaw Kaczysnki. A final result was expected later Monday.
Presidential elections were called following the death of Polish President Lech Kaczynski in a plane crash in April in western Russia.
Kaczynski and dozens of police military, academic and church officials had been en route to a ceremony to mark the anniversary of the Katyn massacre.