* Italy president holds final consultations to pick leader
* PM Renzi resigned after bruising referendum defeat
* Interior Minister says would support a new Renzi government
By Antonella Cinelli and Isla Binnie
ROME, Dec 10 (Reuters) - Political parties made their cases to Italy's head of state on Saturday for candidates to lead the country out of a government crisis prompted by Matteo Renzi's resignation as prime minister.
President Sergio Mattarella, a 75 year-old former constitutional court judge, must decide if someone can lead the country to elections scheduled for 2018, or whether an interim government could serve until early elections in spring.
Italians rejected Renzi's constitutional reform in a popular vote on Dec. 4, leading the 41 year-old to fulfil a pledge to resign as premier if he failed to rally support for it.
Mattarella started with smaller parliamentary groups on Thursday, gearing up to finish with Renzi's Democratic Party (PD), which holds a majority in both houses, later on Saturday.
Interior Minister Angelino Alfano, whose small centre-right grouping in the ruling coalition met Mattarella around midday, said his party would support a new mandate for Renzi, although a parliamentary source said last week the PD leader had ruled out - for the moment - staying on as a caretaker.
"It is important to end this government crisis quickly, because of the urgent pressures we face," Alfano said, listing poverty and deprivation that were highlighted by the referendum result, and the need to prop up fragile banks.
He also said work should start on writing a new electoral law before a constitutional court ruling on the legitimacy of the current one, which is scheduled for Jan. 24.
Three PD lawmakers close to Renzi said that, going into consultations, Renzi's top pick to lead an interim government would be Foreign Minister Paolo Gentiloni.
In this scenario, Gentiloni would oversee the writing of a new electoral law and the PD would hold primaries for candidates to lead the party into elections in spring, the lawmakers said.
But the president may want to ensure the support of former prime minister Silvio Berlusconi's Forza Italia (Go Italy) party, to allow the legislature to last until 2018, one of the lawmakers said, throwing wider the list of possible candidates.
Mattarella is also due to consult later on Saturday with representatives from Forza Italia and the anti-establishment 5-Star Movement, which comes a close second to the PD in opinion polls.
The 5-Star and the anti-immigrant Northern League, which visited Mattarella on Friday, have called for an immediate vote. (additional reporting by Steve Scherer Editing by Jeremy Gaunt)