Rajapakse asked Key to visit the island after the home team crushed England by 10 wickets on Saturday to reach the World Cup semi-finals that will be played at Colombo's Premadasa Stadium, spokesman Bandula Jayasekera said.
The 1996 champions will tackle New Zealand on Tuesday for a place in the finals. The Black Caps had knocked South Africa out of the World Cup by defeating them by 49 runs on Friday.
Sri Lanka's media hailed their side's entry into the semi-finals, but the Sunday Island newspaper said Sri Lankans had dropped several catches and were not at their best.
"How poorly England played yesterday was evident by the fact that it wasn't the perfect game displayed by the Sri Lankans," the Sunday Island said.
Sri Lanka will meet New Zealand for a second time in the current World Cup after their 112 run victory over the Black Caps in their Group A match at the Wankhede Stadium on March 18.
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