Italy's prime minister-designate's efforts to put together a cabinet remain thwarted as his political backers pushed for a eurosceptic economy minister who the president has so far refused to accept.

The possible appointment of the 81-year-old economist Paolo Savona has rattled financial markets. In a further blow to the nascent government, Moody's on Friday threatened to downgrade the country's sovereign debt rating.

President Sergio Mattarella on Wednesday gave Giuseppe Conte, a law professor and political novice, a mandate to form a coalition government with the backing of the anti-establishment 5-Star Movement and the far right League, two rivals, more than 80 days after an inconclusive election.

Conte met the president on Friday without resolving the deadlock over Savona, who has questioned Italy's membership of the euro and attacked Germany for trying to dominate Europe economically.

After the meeting, League leader Matteo Salvini said he was "truly angry" in an apparent reference to the president's veto of Savona.

On Saturday, Salvini did not back down, saying the League had already taken enough "steps backward". He would give Conte a list of the party's possible ministers later in the day.

Asked if he was concerned about a split with the president's office, he said: "The only risk I see is that the people are further distanced from the palaces of power."

Though Savona's possible nomination has worried financial markets, he has distinguished academic and professional credentials with high-level experience at the Bank of Italy and in government as industry minister in 1993-94.

"To veto the economy minister, despite Savona's excellent resume, I find as a citizen to be absolutely unacceptable," Alessandro Di Battista, a top 5-Star politician, said on Facebook.

Mattarella has not spoken publicly about Savona, but through his aides he has made it clear he does not want an anti-euro economy minister and that he would not accept the "diktat" of the parties.

Conte, whose choices for his cabinet must be approved by Mattarella, appeared to be unable to negotiate an alternative as his backers, the League and 5-Star, held the line.

"We're working," Conte said when asked about his progress as he entered the lower house of parliament on Saturday.

If Conte were to fail to come up with a cabinet that gets the blessing of both the coalition and the president, it could force another election later this year.