Italian Interior Minister Matteo Salvini said on Friday that parliamentarians would have "to get off their bums" and return to Parliament for a no-confidence vote after his far-right League party announced it would submit a corresponding motion to the Senate.
"This would be a grave danger for the country", Letta said, while also suggesting that a second government under Prime Minister Giuseppe Conte might be formed, at least until Italy's European Union commissioner was named and Rome's budget for 2020 was adopted.
On Twitter, Salvini wrote that "those would waste time only want to save their seats (in parliament)", in an apparent reference to his governing coalition partner, the populist Five Star Movement.
League senators sought a confidence vote in Parliament on Conte's government that the premier appeared destined to lose, without Salvini's support.
An election could be held as early as October.
"The only thing I am interested in is that we fix a date for the election".
He made his appeal to M5S, Silvio Berlusconi's conservative Forza Italia party, the radical left, the centre-left Democratic Party (PD) and others as parliamentary groups prepare to decide when a motion to censure the government could be voted.
The developments follow Salvini's demand for the prime minister, Giuseppe Conte, to reconvene parliament to collapse the administration.
Backing for Mr Salvini's League has soured over the past year, with recent polls putting it at 36 percent of the vote, with support for M5S dwindling to just 15 percent.
Conte said he would no longer accept Salvini's attacks on his ministers and accused him of relying on "slogans".
Both houses of parliament are now on recess for the holidays and are not due back until September.
"Italy can no longer put up with the no's, we need yes's, we need to unblock, to build, to work - enough is enough, we must go to elections", he told reporters after a rally in Pescara, on the Adriatic coast. "For us the only alternative to this government is to give the choice back to the Italians with new elections".
5-Star became the top party in the general election held in March a year ago.
In the European election in May this year, however, the League took the most votes in Italy with 34 percent.
However, President Sergio Mattarella will ask the parties in parliament to explore ways to appoint a new government, which could prevent early elections.
Besides the high-speed rail-link, the League listed other areas of contention between the two parties, including fiscal policies, energy, justice reform, regional autonomy and relations with Europe. "Of a government of 'No.' This government in reality has always spoken little, and worked a lot", Conte said.