"Significant progress has been made on a cabinet and on appointing a prime minister amid constructive cooperation between the two sides.
"The goal is to finalise everything is as short time as possible to give answers and a democratic government to Italy," said the statement, coming after a meeting at the Italian parliament between Di Maio - who heads Italy's largest party - and Salvini - who leads the biggest political bloc.
President Sergio Mattarella on Monday gave the pair a further day of last-ditch talks on forming a coalition after two months of political deadlock since Italy's inconclusive March 4 election.
The main obstacle to a Five-Star-centre-right tie-up has been Salvini's refusal to break with his veteran conservative ally Silvio Berlusconi, leader of the Forza Italia party who has a tax fraud conviction and is on trial for bribery.
But late on Monday, Berlusconi yielded to pressure, including from his own lawmakers, and pledged that he is open to Five-Star and the League parties governing together.
Mattarella has given Di Maio and Salvini until Thursday afternoon to agree on forming a majority government.
(This story has not been edited by Social News XYZ staff and is auto-generated from a syndicated feed.)
