In a message sent to Dr Singh on Saturday, Gilani said the World Cup has been "successful in bringing the cricketing fraternity even closer and making this sport more popular around the world."
Gilani "expressed the hope that the sports link between India and Pakistan will be fully restored in the near future and the sportsmen of both sides will continue playing their important role for peace, friendship and amity between the people of the two countries".
He also commended the "excellent performance of the Indian team throughout the tournament as well as in the final match."
India on Saturday night lifted the cricket World Cup after a gap of 28 years with a six-wicket victory over Sri Lanka in the summit showdown in Mumbai.
The semi-final between India and Pakistan, which generated exceptionally high excitement and interest among the people of both countries, also provided an "opportunity to their leadership to advance the peace process and build bridges of peace, trust and confidence," Gilani said.
India beat Pakistan in the semi-final at Mohali on March 30 to advance to final with Sri Lanka.
Gilani visited Mohali at Dr Singh's invitation to watch the match. The two premiers also held talks on the margins of the match and agreed to resolve all outstanding issues through dialogue.
