The Five Star Movement (M5S) and the anti-immigrant League party had on Wednesday asked for 24 hours to resolve the stalemate, failing which fresh elections could be held.
M5S leader Luigi Di Maio and League chief Matteo Salvini met at the lower house Chamber of Deputies on Thursday morning.
"Significant steps were made towards the composition of the executive and the nomination of the prime minister," the pair said in a statement after the morning round of talks.
Members of their sides were scheduled to hold further discussions in the afternoon.
They were aiming for an agreement "in a short time-frame to give the country a political government", the statement said.
In a sign of progress on Wednesday, Mr Salvini's right-wing coalition partner, former prime minister Silvio Berlusconi, gave the green light for the pair to form a government without his Forza Italia (FI) party.
Mr Salvini and Mr Berlusconi's coalition won the most seats in the March election, but the 81-year-old ex-premier has been a sticking point in the ensuing horse-trading.
Mr Di Maio insisted Mr Salvini dump the scandal-dogged media mogul Berlusconi and form a government with the M5S and without FI.
Late on Wednesday Mr Berlusconi announced he would not block a possible coalition deal between the two parties.
Between them they would have enough seats in both houses of parliament to form a majority.
After three failed rounds of consultations hosted by President Sergio Mattarella, Italy had looked to be heading either for a caretaker government, chosen by the president, or fresh elections.
Both the League and M5S are staunchly opposed to a caretaker government and without their support the initiative would not pass a confidence vote in parliament.
The alternative could be fresh elections as early as July.
News agency AGI said Mr Di Maio and Mr Salvini were aiming to indicate their choice for prime minister to President Sergio Mattarella by Friday.
Talks over policies will likely take longer given the serious differences between the two parties, in particular regarding the M5S's flagship universal basic income policy.
"We still have to work on the programme, on dates, on the team and the things that need doing," Mr Salvini said.
"Either we reach a conclusion, or we return to the voters."