Fico was elected speaker of the lower house last month in a horse-trading pact that was supposed to smooth negotiations between Five Star (M5S) and the right-wing coalition led by the nationalist League.
However, he now finds himself with an "exploratory mandate" to see if the Democratic Party (PD) will give the M5S a parliamentary majority.
"I will get to work immediately and in my opinion the key point is to begin with issues and the programme in the interests of the country," Fico said to reporters after meeting Mattarella on Monday.
Talks between M5S leader Luigi Di Maio and the League's Matteo Salvini collapsed last week after both refused to budge over Salvini's coalition partner, former premier Silvio Berlusconi.
Photo: Tiziana Fabi/AFP
Di Maio demanded that Salvini dump the 81-year-old media magnate, who the M5S regards as the symbol of political corruption, but Salvini insists he will not break up a coalition that won a combined 37 percent of the vote in March's inconclusive general election.
The M5S is Italy's largest single party with 33 percent.
M5S MP Fico comes from his party's left-wing but his chances of agreeing a government with the PD look even slimmer than they did with Salvini, as the M5S has heavily criticized the caretaker government led by the PD.
Interim PD leader Maurizio Martino has repeatedly refused to act as a "crutch" for a M5S administration and insists that his party will remain in opposition, even if some of his MPs would like to work with Di Maio's party to stop the formation of a government led by the far-right League.