Italian PM-designate Giuseppe Conte has given up his bid to form a government after the country's president vetoed his choice of economy minister.
President Sergio Matarella said he had agreed to all proposals but could not back Paolo Savona, a eurosceptic.
Mr Matarella's move angered populist parties trying to form a coalition. Luigi Di Maio, the leader of 5-Star, called for the president's impeachment.
Italy has been without a government since elections on 4 March.
Two populist parties, 5-Star, which won 32% of the vote, and the far-right League party, which won 18%, had agreed earlier this month after days of talks to form a coalition.
There is now a real argument in Italy between the president and the populists about this country's position in the EU, the BBC's James Reynolds reports from Rome.
As a stopgap move, the head of state has summoned former International Monetary Fund (IMF) economist Carlo Cotarelli potentially to take over as a non-populist prime minister.
But this appointment may not last and the only immediate solution may be an early election in which, all of a sudden, Italy's membership of the euro and its relationship with the EU itself really are up for discussion, our correspondent adds.
What just happened?
Mr Conte, a political novice, was proposed by the two parties as prime minister in an attempt to break Italy's 11-week political deadlock.
He went to meet Mr Mattarella to put forward picks for his cabinet but the president vetoed Mr Savona as finance minister, citing his fierce opposition to the EU.
Under Italian law, the president has the right to reject the appointment of a cabinet member but his decision was a controversial one.
Mr Di Maio called for impeachment under article 90 of the constitution, which allows parliament to demand a president step down based on a simple majority vote.
If a vote were to be successful, the country's constitutional court would then decide whether to impeach or not.
"After tonight, it's truly difficult to believe in the institutions and the laws of the state," Mr Di Maio said.
What happens next?
Mr Mattarella said he had "agreed and accepted all the proposals except that of the economy minister".
"No-one can claim that I have stood in the way of the formation of the so-called government for change," he said.
He said he would wait before deciding whether to call fresh elections, and summoned Mr Cottarelli for talks on Monday.
Mr Cottarelli, 64, worked at the IMF from 2008 to 2013, gaining the nickname "Mr Scissors" for making cuts to public spending in Italy.
What else are the parties saying?
Mr Di Maio said Mr Mattarella's rejection of Mr Savona was "unacceptable".
"It's an institutional clash without precedent," he said in a live Facebook video.
Matteo Salvini, leader of the League, called for a new election.
"In a democracy, if we are still in democracy, there's only one thing to do, let the Italians have their say," he told supporters in a speech in central Italy.
What do the markets make of the crisis?
Mr Savona, who served as industry minister during the 1990s, has been an outspoken critic of the EU and an opponent of austerity programmes, prompting concern over the proposed government's commitment to the EU and ability to rein in the country's massive national debt - equal to 1.3 times its annual output.
The League had proposed to cut personal and business taxes and roll back planned pension reforms designed to cut government spending, at a cost running into tens of billions of euros.
President Mattarella warned on Sunday that the prospect of a populist government had "alarmed Italian and foreign investors" and worsened the "spread" - the gap between Italian and German 10-year government bond yields.
The spread rose to 215 basis points on Friday - the widest in four years. Ratings agency Moody's warned that it might downgrade Italy's sovereign debt rating to "Baa3" - one notch above the junk rating.