Critics of the new government say that the strongest bind between the new coalition partners is a shared antipathy toward Mr. Salvini and the League — which became the biggest party in the European elections in Italy last May and still polls strongly nationally — and a mutual aversion toward new elections, which they would be likely to lose.

The antipathy flows both ways. On a popular late night talk show on a state-owned channel, Mr. Salvini said, “Treason doesn’t pay, and time is on our side.” He added that “this is the least popular government in the history of Italy’s Republic.”

According to one survey released on Monday, the League would take 33.4 percent of the vote in the event of a national election, with its hard-right allies, the Brothers of Italy, at 7.2 percent. The Democrats polled at 22.1 percent and Five Star at 21 percent, down significantly from the March 2018 election in which it won 32.2 percent.

Mr. Conte became prime minister in 2018 as a consensus candidate with no party affiliation or government experience. But a year in the post appears to have honed his political skills, and he has deftly managed the crisis that began last month when Mr. Salvini pulled his support from the government to try to force elections.

Instead, Mr. Conte persuaded Five Star, to whom he is close, and the Democratic Party to overcome their mutual dislike to form a coalition. Five Star’s political leader, Luigi Di Maio, was named foreign minister in the new cabinet and will often cross paths with the incoming European Union commissioner for economic affairs, Paolo Gentiloni, who preceded Mr. Conte as prime minister.

Shortly after his nomination in Brussels on Tuesday, Mr. Gentiloni said he intended to focus on kick-starting growth in Europe and on “social and environmental sustainability” in the bloc. He is also expected to take up Rome’s call for a relaxation of European Union fiscal rules that critics say stifle expansion.

Mr. Conte said that Italy would also ask Europe to increase its investments in Africa and intensify cooperation there, a step toward slowing down the flows of immigrants who try to cross the Mediterranean in search of a better life in Europe.