Mattarella confirmed that the nomination by Five Star and the League of Paolo Savona for economy minister saw the end of Conte's brief mandate.
In his latest book, "Like a Nightmare and a Dream", 81-year-old Savona calls the euro a "German cage" and says that Italy needs a plan to leave the single currency "if necessary".
Conte's decision to step aside leaves Italy in a political crisis almost three months after March's inconclusive general election.
Italian media speculated that, in the meantime, Mattarella could try to appoint a technocratic government.
The leaders of the two parties trying to field a government, the far-right League and anti-establishment 5-Star Movement, accused President Sergio Mattarella of abusing his authority and working under the orders of European powers.
Shortly afterwards, he summoned former International Monetary Fund (IMF) senior official Carlo Cottarelli for a Monday morning meeting - an indication he may be considering asking him to head a government of unelected technocrats. "The uncertainty about our position in the euro has alarmed Italian and foreign investors who have invested in our bonds and companies", Mattarella said.
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The 5-Star's Di Maio also demanded impeachment under article 90 of the constitution.
"I am very angry", Di Maio said.
Four days earlier, Conte, a little-known academic, had been granted the opportunity by Mattarella to draw up a list of ministers and attempt to form a government.
Conte's rejection paves the way for a new government crisis that could lead the country to a new election.
The leaders of Five Star and the League, Luigi Di Maio and Matteo Salvini, were infuriated by Mattarella's refusal to accept Savona, a respected financier and economist.
"If there's not the OK of Berlin, Paris or Brussels, in Italy a government can not be formed". We'll change this Country, together. Polls in Italy since indicate that the parties' support has held steady or grown. But they are gate-crashers in Italy's national politics, and on Sunday, former prime minister Matteo Renzi, a member of the Democratic Party, wrote on Facebook that Di Maio and Salvini had taken Italy hostage "for three months".