A rift between the two coalition partners, Five Star Movement (M5S) and the Lega, deepened this week after the M5S voted against a costly Turin-Lyon high-speed rail link project (TAV) backed by Salvini's party.
"Today, I told Prime Minister Conte: let's go straight to the parliament to record that there is no majority anymore, as the TAV vote showed, and quickly give the floor to the Italians," Salvini said in a statement.
Italians need certainty and a government that is productive, he stressed.
"We do not want any more seats or ministers, we do not need reshuffles or technical governments. After this government, which has done a lot of good, there can only be election. [Summer] recess cannot be an excuse for losing time, and parliamentarians, unless they want to save their mandate by any means, can return to work next week, like millions of other Italians," Salvini said.
The parliament's recess started on Thursday and is scheduled to conclude in early September.
M5S leader Luigi Di Maio said that his party was ready to participate in snap parliamentary elections.
"We are ready, we are not at all interested in the [ministerial] seats, and they never interested us," Di Maio said a special statement circulated on Thursday evening.
He also proposed to finally approve the law on reducing the composition of the Italian parliament by half before conducting the snap election. The final vote on this issue was scheduled for early September, immediately after the recess.
"This is a landmark reform, we will reduce 345 seats and send home 345 politicos. If we again convene the chambers of parliament, we will take the opportunity to vote on this reform earlier. We will vote for it and then pass the floor to the Italians," Di Maio said.
The leader of the largest opposition Democratic Party, Nicola Zingaretti, also said that his supporters were ready for early elections.
"We are ready for the challenge. In the upcoming elections, not only the issue of government will be decided, but also the fate of our democracy and the international position of our country," he wrote on Facebook.
On Wednesday, Salvini said that "something is broken" in the government coalition, while Di Maio wrote on Facebook that he was "tired of palace games." Sources in M5S said it opposed the "technical government," which, in the absence of a parliamentary majority, could survive until the next election.
On Thursday morning, Conte held consultations with President Sergio Mattarella. After the meeting, it was reported that Conte and Mattarella discussed neither the government crisis, nor the prime minister's departure. Conte later held separate meetings with Salvini and Di Maio.