"Staying out of politics is a fair request because Mattarella wants to be sure that whatever the Cottarelli government does, it will not be as a way to further political ambitions", Ugo Arrigo, a professor of economic sciences and statistics at Milan Bicocca University, said in an interview.
Meanwhile, Cottarelli also underlined the importance of dialogue between the European Union and Italy - a founder member - and of Italy's continued membership of the euro. The euro touched a fresh six-month low and yields on Italian debt climbed, increasing the extra borrowing costs or spread that Italy pays in comparison with Germany. These could take place after summer but may not happen until next year.
The government's benchmark borrowing rate increased further, a sign of caution, even after Mr Cottarelli was tapped.
The head of the anti-establishment 5-Stars, Luigi Di Maio, had proposed a renewed effort to form an alliance with the right-wing League on Tuesday night, backing off his threat of launching impeachment proceedings against Mattarella and insisting that the two blocs still enjoy a parliamentary majority. Italy is used to short-lived governments - it has churned through 65 of them since the end of the Second World War - but this particular one did not even get officially installed before it blew up.
"Why don't we just say that in this country it's pointless that we vote, as the ratings agencies, financial lobbies decide the governments?" he asked in a video on Facebook. League chief Matteo Salvini threatened mass protests unless snap elections were called.
Since the March 4 elections in Italy, day-to-day governance is still in the hands of outgoing prime minister Paolo Gentiloni. Five Star was down to 29.5 per cent from 32.7 per cent. Forza Italia was down to 8 per cent from 14 per cent.
Of course the spread between yields on government bonds can not "conspire" against anyone because spreads are just numbers and numbers, by virtue of being numbers, can not have a sense of objective. It was down 0.7 per cent as of 10:48 am in Rome. And equities were hit hard, led by bank stocks.
Carlo Cottarelli addresses a press conference at the Qurinale presidential palace on May 28, 2018 in Rome after Italian President gave him mandate to form a government.
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The caricature of the ugly German matched that of the lazy Italian, which ran through the German media in the past few days as the populists were on the verge of taking power with a plan to provide fiscal stimulus to Italy's ailing economy. Between now and new elections, perhaps in September, the populists are threatening in effect to campaign against the country's very system of government.
The rare move by the president sparked fury from both parties, who say they will reject Mr Cottarelli's nomination in parliament.
Looking to allay investor concerns, Mattarella vetoed on Sunday the choice of 81-year-old economist Paolo Savona, a vocal critic of the single currency, to the pivotal economy post.
After that, Mr Mattarella would dissolve Parliament and set elections for 2019, Mr Cottarelli said.
The commentator predicted the impeachment threat against the president "who only was defending his institutional role and the Constitution is only a taste of what will come".
The Neue Zürcher Zeitung commented, "Now the populists bitterly accuse the president of undermining democracy and freedom in Italy and conjure up a 'conflict between the people and the palazzo.' Their followers are already posting poisonous messages against Mattarella on the Internet".
While Mr. Di Maio, 31, and Mr. Salvini, 45, called for Mr. Mattarella's ouster, European investors were happy, at least initially.
Cottarelli served in the broad-based Enrico Letta government in 2013 and found €32 billion ($37 billion) in cuts, not all of which were implemented.