On January 25, Libyan lawmakers voted to reject the Government of National Accord (GNA) endorsed by the UN Security Council.
"We expect that the proposals on the new Libyan government will be presented before the parliament on Tuesday," Gentiloni said at a joint press conference with US State Secretary John Kerry.
Under the UN Libyan Political Agreement, the Presidency Council formed in mid-December announced a Cabinet of 32 ministers on January 19.
On December 23, the UN Security Council backed the agreement, aiming to form a government in Tripoli within 30 days.
The Tobruk-based legislature is the internationally-recognized rival to the government based in Tripoli, the traditional capital of the North African state, which has been in political and security turmoil since 2011.
The Presidency Council has reportedly been given 10 days to assemble a new Cabinet of no more than 17 ministers.