Mattarella faced impeachment calls after refusing on Sunday to accept the nomination as economy minister of Professor Paola Savona, an 81-year-old economist who has called Italy's entry into the euro a "historic mistake".
The president's move pitted him against the democratically elected populist winners of March elections, with the far-right League and anti-establishment Five Star Movement enraged by the decision. Most analysts however say a call for Mattarella's impeachment by Five Star leader Luigi Di Maio, has little chance of success since it is only possible in cases of "high treason" or for "acting against the constitution".
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"President Mattarella has only exercised his constitutional powers", said Massimo Luciani, president of the Italian Constitutionalists Association.
Demands to "impeach" Mattarella have no substance as he used his powers "like other presidents before him". said Holger Schmieding, chief economist at Berenberg,
Balance of power
The Italian president's role is largely ceremonial but also includes the power to appoint the government.
In a country which has had 64 governments since World War II, their role as a referee above the political fray has often been viewed as essential, and strengthened the president's image as a guarantor of the country's stability.
"(If Mattarella) had given in, bowing to the threats, the balance between the powers of the state would have been brutally broken," wrote left-wing newspaper La Repubblica.
But Il Fatto Quotidiano newspaper, close to the Five Star Movement, wrote: "King Sergio blows up everything".
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Italy has a government debt burden of 2.3 trillion euro ($2.7 trillion). Mattarella justified his veto decision by citing concern from investors at home and abroad over the nomination of fiercely eurosceptic Savona and the possible impact on the markets.
Instead the president has nominated Carlo Cottarelli, a pro-EU, International Monetary Fund (IMF) veteran, to head a caretaker government which may only last through August after which elections will likely be held.
Known as "Mr Scissors" for making cuts to public spending in Italy, Cottarelli is a deeply unpopular pick among Five Star and League members, whose hopes of forming a coalition have been shattered, at least for now.
'Lack of legitimacy'
Nobel economic laureate Paul Krugman warned that the political developments in Italy could have implications for the whole EU project.
"Faith in the single currency trumps democracy? Really?" he wrote on Twitter.
"European institutions already suffering lack of legitimacy due to democratic deficit. This will make things much worse."
Eurosceptic politicians from across the continent also condemned the developments in Italy.
"The European Union and the financial markets are again confiscating democracy. What has happened in Italy is a coup d'état," French far-right leader Marine Le Pen wrote on Twitter.
Leading Brexit campaigner and former leader of the UK Independence Party, Nigel Farage, said on Twitter: "Italian voters will be furious that the establishment is blocking new ministers. Time for more elections and bigger votes."
But others praised Mattarella's stance. French President Emmanuel Macron, a pro-Europe centrist, said his Italian counterpart was fulfilling his role as the guarantor of the country's institutions with "courage and responsibility".
By Olivier Baube