UPDATE 3-Russia state oil company to explore for oil in Cuba

* Russian firm gets two onshore, two offshore blocks

* State oil company Zarubezhneft wants more turf

* Company's general director sees "good prospects" (Adds Cuba minister quote, details, minor edits)

By Marc Frank

HAVANA, Nov 3 (Reuters) - Russian state oil company Zarubezhneft signed contracts with Cuba on Tuesday to search for oil along Cuba's northern coast and said it was looking at procuring more areas for exploration in a step forward for the island's oil hopes.

Zarubezhneft signed up with state-owned Cuba Petroleos for four almost contiguous blocks, two onshore and two offshore in the Gulf of Mexico just east of Cuba's most prolific oil field in Varadero.

Cuba has signed offshore exploration deals with eight other companies, but waters it says may hold 20 billion barrels of oil remain untapped, with only one test well drilled.

Big oil finds in the gulf could turn the communist island, which is deep in financial crisis, into an oil exporter.

The Zarubezhneft deal with Cuba was the latest sign of warming relations between the Cold War allies, who had a falling out after the Soviet Union, Cuba's biggest benefactor for 30 years, collapsed in 1991.