President Sergio Mattarella gave Conte a mandate on Thursday to try to form a new coalition following Matteo Salvini’s decision to pull his right-wing League from its 14-month-old alliance with the M5S in an attempt to force snap elections.
Talks between the M5S and the PD resumed on Saturday after a squabble that had threatened to stop the potential coalition in its tracks.
Tensions remained, however, on the issue of migration.
The M5S has insisted a controversial law – crafted Salvini – banning charity ships which rescue people in the Mediterranean from docking in Italy should not be altered or scrapped by the new government.
PD leader Nicola Zingaretti, however, called for people trapped in limbo at sea on rescue ships to be given shelter.
On Friday the M5S – which has far more seats in parliament than its new ally – had warned that the deal could still fall apart, should the PD not agree to a list of key demands.
The suggestion by M5S leader Luigi Di Maio that he was ready to pull the plug and return to the polls alarmed the markets and angered the PD.
But just hours later the parties appeared once again set on a collision course.
If all goes well, Italy could have a new government by Wednesday.
If no agreement is sealed in the coming week, Mattarella is expected to dissolve parliament and set a date for new elections.