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The star claimed that Penn helped him to turn his life around during his well-documented problems in the mid-1990s, WENN reports.
Rourke has been nominated for his part in Darren Aronofsky's The Wrestler while Penn is up for the same award for the title role in the biopic Milk.
"Sean Penn is a good friend of mine," Rourke said.
"When I was down and out, he got hold of me and told me exactly what to do and not to do. I owe him so much that I hope he wins the award."
Earlier this month, it was claimed that Rourke and Penn had resolved their differences over drinks at the Sunset Tower in Hollywood, following reports that Rourke had previously called Penn homophobic.
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