"Together with international organisations, namely Nato and our allies, we will aim to set an end-date for this mission," Frattini told journalists in Rome
He had been asked to comment on remarks made Tuesday by Italian vice-admiral Rinaldo Veri, commander of the Nato's air and naval operation in Libya suggesting an open-ended operation.
Veri had said the operation would "last as long as necessary" and until Libyan strongman Muammar Gaddafi stopped bombing civilians and his soldiers "withdrew to their barracks to allow humanitarian aid in".
The UN Security Council adopted a resolution imposing a no-fly zone over Libya on 17 March, paving the way for a military operation against Gaddafi which began two days later and is mandated to "take all necessary measures to protect civilians."
The command of the operation was shifted from a US-led international coalition to Nato in late March.
The Italian government belatedly decided to join the military campaign against Gaddafi in late April, a move vehemently opposed by its Northern League ally, whose leader has threatened to bring the government down over the air raids.
The xenophobic coalition partner says the air strikes will trigger a wave of illegal immigration from Libya to Italy's southern coast, and is demanding Berlusconi set a date to end the raids.
Umberto Bossi, the pugnacious Northern League leader threatened to bring down the fragile government if parliament was not allowed to vote on the issue.
Interior minister Roberto Maroni, another Northern League figure, predicted the government would fall if the bombing was not stopped.