ROME — Days after taking office, the two pillars of Italy’s first populist government led rallies Sunday in Sicily, where they detailed their strategies for deporting migrants and enacting other campaign promises that helped put them in power.

Matteo Salvini and Luigi Di Maio, the leaders of the right-wing League and the euroskeptic Five Star Movement, want to capitalize on the momentum of their coalition government taking national office Friday.

But with each man emphasizing different priorities, there are doubts if the new government, led by a political novice with Five Star sympathies, Giuseppe Conte, will last a full five-year term.

During the campaign, the League stoked fears about migrants, who have arrived in large numbers in Italy. Mr. Salvini, the interior minister in the new government, vowed to expel them en masse, dismissing logistical challenges and costs.