Political clashes over the project for a railway between the Italian city of Turin and French city of Lyon led Prime Minister Giuseppe Conte to put tenders on hold in March.
The multibillion-euro TAV (Treno Alta Velocità) link involves digging a 58km (36-mile) tunnel through the Alps.
It is bitterly opposed by Five Star on environmental and cost grounds.
The League argues that it would create jobs and stimulate economic growth, and that moving freight from road to rail is environmentally friendly.
Supporters of the project say it would halve the travel time between the two cities to just two hours. The tunnel would also make it possible to travel from Paris to Milan in around four hours, down from nearly seven.
The project was launched 20 years ago and part of it has already been dug. It is scheduled for completion in 2025.
Costs were initially projected to hit €8.6bn ($9.7bn; £7.4bn), but Italy's Transport Minister Danilo Toninelli - a Five Star member - put the price tag at over €20bn.
The EU pledged to fund up to 40% of the cost.
What happens now?
"Let's go straight to parliament to say there is no longer a majority... and quickly go back to the voters," Mr Salvini, who is both deputy prime minister and interior minister, said on Thursday.
Mr Di Maio, who is also a deputy prime minister, countered by declaring in a statement: "We are ready, we don't care in the least about occupying government posts and we never have."
While the League is the junior party in the coalition, it came first in the European elections in May, taking more than a third of the vote.
It has been in an uneasy coalition with Five Star, which came to power on an anti-establishment ticket. Giuseppe Conte, a non-party law professor, serves as prime minister.
Mr Salvini's demand for an election does not necessarily mean a poll will be called in the near future.
President Sergio Mattarella could theoretically appoint a government of technocrats and postpone a new election until next year.