Italy's anti-establishment Five Star Movement (M5S) has issued a long wish list of requirements for any new government coalition during talks with President Sergio Mattarella, after the center-left Democratic Party (PD) extended its own set of demands for any tie-up with the populist group it has criticized and bitterly opposed for the best part of a decade.

Prime Minister Giuseppe Conte resigned earlier this week as a fragile coalition between the anti-immigration Lega party and the M5S finally cracked. The country's future is now in the hands of Mattarella who is holding consultations to see whether any parties can form a majority — with an M5S-PD pact looking the most likely at this stage.

The unlikely alliance would in theory enjoy a relatively comfortable majority in the parliament's lower house, the Chamber of Deputies, but would rely on a handful of sympathetic but unaligned senators if it were to win votes in the upper legislative chamber.

And analysts have said the chance of that stability may have helped Italian bond yields remain relatively subdued this week, but the country's debt pile means investment risks remain high ahead of a review of the country's sovereign debt rating by Moody's in early September.

"This crisis must be solved with a clear and prompt decision," Mattarella said after two days of meetings with each of the country's party leaders. He said this was "necessary for the economic and political uncertainties at the international level," as global growth falls and geopolitical tensions within and beyond Europe remain elevated.

He has given the two parties until Tuesday to try and formalize an agreement that might allow him to anoint a new prime minister to form a government, and thus prevent fresh elections that would take place less than two years since the last national vote.