Italy's Mario Draghi has begun detailed talks on the formation of a new government, a day after being parachuted in to restore political order in the country.

The former president of the European Central Bank (ECB) was scheduled to meet party leaders in Rome to sound them out about their willingness to support a national unity administration.

Outgoing Prime Minister Giuseppe Conte, in his first remarks since leaving office last week, said he met Mr Draghi today and wished him "good luck". 

Mr Conte said the country needed "a political government that is solid and sufficiently united" to tackle the urgent crisis brought on by the coronavirus pandemic.

Mr Draghi has support from some of the main parties in parliament, but the biggest, the populist Five Star Movement (M5S) that strongly backed Mr Conte, is not yet on board.

The economist's task is urgent, Italy remains in the grip of the deadly coronavirus pandemic, with the death toll still rising by hundreds each day, to a total of almost 90,000 so far.

The government must also come up with a plan within weeks to boost its recession-stricken economy with the help of a massive injection of European Union funds.

Giuseppe Conte addressing the media outside Chigi Palace in Rome

According to the daily La Stampa, Mr Draghi faces a "puzzle". 

The PD and ex-premier Matteo Renzi's Italia Viva party are ready to back him, alongside Silvio Berlusconi's opposition conservative Forza Italia and some smaller left and centrist forces.

Mr Renzi, who triggered Mr Conte's resignation by pulling out of the ruling coalition, told the daily La Repubblica that the Draghi government "will be the salvation of Italy."

However, to take office, Mr Draghi also needs the abstention or the support of one of three other parties: M5S, Matteo Salvini's far-right League and the Brothers of Italy, also far right. 

Even if it has lost most of its radical edge, the M5S started out as an anti-elitist party, so it is ideologically awkward for them to endorse a quintessentially establishment figure like Mr Draghi. 

One of the M5S leaders, outgoing Foreign Minister Luigi Di Maio, echoed Mr Conte's call for a "political government", rejecting the idea of a cabinet made up of technocrats.

Mr Draghi could get around that by offering some cabinet posts to the M5S and other parties, but it remained unclear whether this would be enough to overcome the blockage.

Mr Di Maio and other members of the outgoing administration were being considered for new cabinet positions, according to multiple media reports. 

Mr Conte, a law professor plucked from obscurity when he first became premier in 2018, hinted he would stay in politics, telling his M5S supporters: "I am here, and will remain here."

The PD's Roberto Gualtieri could also survive as Economy Minister, even if Carlo Cottarelli, a former IMF official, and Fabio Panetta, a central banker like Mr Draghi, were also linked to economic portfolios.

Italy is banking on receiving the lion's share of the EU's post-virus recovery fund, around €200 billion, but must submit a credible spending plan to Brussels by April.

Should Mr Draghi fail to muster a majority, or lose a parliamentary confidence vote after taking office, the fallback option would be snap elections, which a right-wing bloc led by Salvini would be favourite to win. 

But President Sergio Mattarella clearly said Tuesday he wants to avoid early polls, given the complexity of holding them in the middle of a pandemic. 

The president called on Mr Draghi yesterday, giving him a mandate to form a government, after repeated attempts to revive the old ruling coalition under Mr Conte failed.