Conte made the ultimatum during a news conference that was carried live on Italian TV. He was responding to increasing tensions between the right-wing League and the populist 5-Star Movement, the parties that formed a coalition government after national elections last year.
Conte, a university professor who was a political novice until the parties agreed to make him premier, said League leader Matteo Salvini and 5-Star leader Luigi Di Maio must stop squabbling or he will offer his resignation.
He demanded a "clear, unequivocal and also fast" answer from the two, "because the country cannot wait." Salvini responded on Twitter, saying "We are ready, we want to continue and we don't have time to waste."
There was no immediate comment from Di Maio. Salvini and Di Maio have been at odds over a range of issue, including taxes, security and a high-speed railway line to France. Tensions rose in the runup to last month's European Parliament elections, in which Salvini's party ultimately made strong gains and the 5-Star Movement lost support.
Salvini often speaking on behalf of the government on issues as if he were the prime minister instead of interior minister hasn't made Conte's any easier. Most recently, Salvini challenged European Union fiscal rules and announced new measures that would increase next year's budget deficit.
The EU's executive commission last week sent the Italian government a letter, a first step toward possible sanctions, saying the country had made insufficient progress toward reducing public debt levels this year.