PARIS - France's new prime minister should come from the left and any coalition government must commit to pension changes and helping with the cost of living, the Socialists said ahead of new talks with the president and other parties on Tuesday.

       In a letter to President Emmanuel Macron, posted on X ahead of the talks at the Elysee palace, Socialist party chairman Olivier Faure repeated his threat that he'd immediately quit talks should Macron appoint another right-wing premier.

       The centre-left Socialists are seen as a likely kingmakers in Macron's bid to form a new government with sufficient parliamentary support to make sure it wouldn't be toppled like the last cabinet under veteran conservative Michel Barnier.

       Faure said that any guarantees not to vote the next government out of power, referred to as "non-censure" agreement, would depend on "a genuine shift in political direction".

       He cited pensions and the cost of living among his priorities, saying "we stay true to the mandate our voters have given us" despite increasing signs the all-left electoral alliance known as New Popular Front might fall apart should its more moderate factions join the government.

       "I urge them not to give in to the temptation of a government of national unity and a grand coalition," Manuel Bompard, a leader of the more hardline, far-left France Unbowed (LFI) party told France 2 television.

       Macron will meet with political parties open to compromise on forming a government at 1400 CET (1300 GMT) on Tuesday, the Elysee said on Monday. A source close to Macron said neither the far-right National Rally party nor LFI wanted to be invited. REUTERS