The government of embattled Italian prime minister, Enrico Letta, looked close to collapse as he dug in his heels in the face of an increasingly formidable threat to his premiership from the leader of his centre-left party.

Letta said it was "not in [his] DNA" to break with the agenda of his government and challenged Italy's political players – chiefly Matteo Renzi, his ambitious young rival – to "lay their cards on the table".

Less than 10 months after it was born from the inconclusive mess of last February's general elections, long-running criticisms of the coalition government's lacklustre record gathered force, putting Renzi, the 39-year-old mayor of Florence, in a leading position to take over as prime minister in an election-free process branded by the media as la staffetta – the relay.

The situation was opaque and the likely outcome of the power struggle unclear . The large national committee of the Democratic party (PD) was due to meet on Thursday to deal with the issue, possibly even putting it to a vote. Giorgio Napolitano, the 88-year-old president whose role it is to appoint prime ministers, has made it clear that the party must give a clear sign of what it wants.

In a message posted on Twitter, Renzi said he would "say what I have to say" before the PD, "live-streamed, in the open". Earlier, the sharp-talking politician had arrived at the doors of Palazzo Chigi in a small blue Smart car for a meeting with Letta which the premier said was "as you [journalists] say, 'frank'".

Speaking of the PD meeting, the prime minister added: "I am simply asking for clarity ... Resignations aren't handed in because of gossip or ruses… I think everyone should express themselves explicitly. Everyone should say what their intentions are." Especially, he added, if that person was looking to fill his shoes.

Ever since he won the primary elections for the PD leadership by a landslide in December, Renzi – a politician viewed as refreshingly energetic by his supporters and insufferably brash by his critics – has kept up regular attacks on Letta's government from the sidelines, pointing out its failings and urging it to do more, particularly focusing his energies on pushing through a new electoral law.

But, until recently, the idea of taking over from his colleague without first going to the polls is not understood to have been considered a viable option. Were he to take over the reins in a staffetta, he would become Italy's third unelected prime minister in under three years, after Mario Monti was brought in to head a technocratic government at the end of 2011 and Letta was put in charge of his awkward coalition with Silvio Berlusconi's centre-right party last April.

According to opinion polls, it is not a move many Italians support, despite their approval of Renzi himself, with an unofficial survey on the television station SkyTG24 showing 74% against a possible takeover and 26% in favour. But Napolitano, who has the final say, is understood to want to avoid snap elections under the old, dysfunctional electoral law, at all costs.

A source in Renzi's circle, who did not want to be named, said:"For Matteo, it's a big risk. A very big risk. But I think it's the only real chance we have of reforms." The PD leader would manage it, the source added, "but it's a real tug of war."

A pro-Renzi MP in the PD agreed it was a high-stakes strategy on the leader's part, but added: "It would also be a big risk to wait a year and then go to an election without having concrete results to show for it."

After a day of feverish speculation, and a face-to-face meeting with his challenger that apparently served only to entrench both men in their opposing positions, Letta went ahead with a press conference evening to unveil what he said was a new coalition pact for a revamped government in 2014. How long it went on for, he said, was entirely linked with how long it would take to carry out the institutional and economic reforms that Italy needed.

He was still working with "determination", he said, defending his record and insisting that, if time had been wasted over the past nine-and-a-half months, "it is not my fault".

Until the autumn, the PD's major coalition partner was Berlusconi's then centre-right party, the Freedom People (PdL), a combination that did not make for easy-going and focused reform. The former prime minister and media mogul later withdrew his support from the coalition and reformed his Forza Italia party in opposition.

Recalling the "crisis situation" in which his government was formed last year, Letta said he had always considered it to be "a government of service" and appeared at pains to stress how unusually difficult his period as prime minister had been, repeatedly declaring he had been living "each day as if it was the last".

"It would be absolutely paradoxical and contradictory and absolutely is not part of my DNA to break with the continuation of a spirit which I consider, even now, deeply linked to the service of the country and not linked to my personal prospects," he said. "My personal prospects do not enter into this affair at all."

But, despite his assurances, Letta, a 47-year-old former minister and MEP, appeared increasingly isolated. A PD MP who did not back Renzi in the primaries said that even the mayor's internal opponents had come round to the idea of him taking over. "By now this is quite a widely held position," he said, speaking on condition of anonymity. "Let's say that [Renzi] has been very good at dealing with many of our proposals, for example on the electoral law, and obviously we are all embarrassed by the slowness of the Letta government in recent weeks. So unfortunately we too are quite critical."

It has been claimed, however, that, rather than finally coming round to him as the leader they need, Renzi's foes may be seeking to tarnish his golden boy image by getting him to take a poisoned chalice which could damage his promising career for a long while to come.

Bill Emmott, the former editor of the Economist and co-writer of a recent documentary on Italy, remarked that, rather than a relay, the mooted move could be more of a hospital pass.

Political rivals

Matteo Renzi, aka The Scrapper

Age: 39

From: Florence

Current role: Leader of Democratic Party; mayor of Florence

Previous experience: President of Florence province

Enrico Letta

Age: 47

From: Pisa

Current role: Prime minister of Italy

Previous experience: Ex-industry minister and european affairs minister; ex-MP and MEP; former deputy leader of Democratic Party