Salvini and Di Maio's 90-minute meeting took place "in a canteen in central Rome and lasted about an hour and a half.
"Things are moving forward and discussions are centred on the final details ahead of a meeting with President (Sergio) Mattarella," said the statement.
"I met Salvini. We are trying to form a government," Di Maio told reporters as he arrived at the Italian lower house of parliament.
Di Maio and Salvini on Monday unveiled their pick of a premier to lead their nascent government - little known Italian law professor and political novice Giuseppe Conte - and on Tuesday held a meeting with the academic.
It is understood Mattarella has significant reservations about the direction of the planned populist government and on Tuesday he convened a meeting with the leaders of Italy's two houses of parliament.
The League and Five-Star issued their joint coalition plans last week which include a 'flat tax', a guaranteed minimum income and cancelling sanctions against Russia.
The common agenda rejects European Union austerity and wants to renegotiate Italy's debt, putting Italy on a collision course with Brussels.
The two Eurosceptic parties won over half the votes in Italy's inconclusive March 4 national polls that led to a hung parliament.
Several previous rounds of talks with Italy's political leaders have collapsed amid a mesh of seemingly irreconcilable demands.
Five-Star is the biggest party while the centre-right alliance, led by Salvini, is the largest political bloc.
(This story has not been edited by Social News XYZ staff and is auto-generated from a syndicated feed.)
