The request came Wednesday night in a letter from the foreign ministry to the British government about the incident, The Daily Telegraph (Britain) reported.
On Monday, the cemetery, which is the resting place of 237 Argentine combatants who fell during the Falklands War, was found vandalized. A glass case surrounding a figure of Argentina's patron saint, the Virgin of Lujan, was smashed.
The foreign ministry said it "repudiated the desecration" of the monument and called for "impartial investigation that identifies and punishes those responsible for a grave act that violates the sacredness of the cemetery."
"Deplorable actions such as these can be avoided through dialogue," the foreign ministry's letter said.