He said he gave the parties extra time, and gave Mr. Conte the mandate as prime minister, “overcoming any perplexity on the fact that a political government was to be led by a president who was not elected in Parliament.”

The president said that he had gone out of his way to accommodate the parties’ choices but that his constitutional role of guarantor had required him to oppose their choice of an economics minister who followed a line “that probably, or even inevitably, would lead Italy to exit the euro.”

While Mr. Mattarella did not say the name of the populist alliance’s choice, he is Paolo Savona, an 82-year-old economist who has lamented Italy’s joining the euro. Mr. Mattarella said that such a pick would alarm Italian and foreign investors and that the already sharp increases in the spread between German and Italian bond yields “increases our public debt and reduces the possibilities of the state to invest.”

He said he could not allow stock market losses to torch the savings of Italian companies and families or make it harder for Italians to borrow money.

“It is my duty, in fulfilling the duty of nominating ministers, which the Constitution entrusts to me, to be careful to safeguard the savings of Italians,” he said. “In this way Italian sovereignty is concretely reaffirmed.”

But Matteo Salvini, the leader of the League, argued exactly the opposite on Sunday night.

Saying he was as angry as “a beast,” he offered a preview of what is likely to be a long and vicious campaign attacking foreign interests, Italian institutions and Mr. Mattarella himself.

“Does this seem like democracy to you?” he said to reporters. He blamed bankers, Brussels, German politicians in Berlin and “the big powers” for blocking the formation of a government and asserted that “Italians would not be anyone’s slave.”