Monte dei Paschi di Siena (MPS) executives are fighting to salvage a multibillion-euro rescue by private investors in a frantic attempt to prop up the bank.

In a statement released after a board meeting on Sunday, the world's oldest bank said it would forge ahead with a debt-for-equity swap offer for tens of thousands of retail investors. The offer still requires regulatory approval. If MPS manages to convince investors to go along with the plan, it would help it avoid a government bailout by Italy, which would have far-reaching economic and political consequences.

A deal to prop up MPS was thrown into doubt last week after the European Central Bank (ECB) reportedly said it could not have more time to secure the private investment. MPS had sought an extension until 20 January.

Markets are now waiting to hear the future of a planned €5bn (£4.2bn) cash injection by private investors to rescue the bank by 31 December.

Reports of the ECB's decision, which were released on Friday and not publicly confirmed, have raised fears that MPS would not be able to secure the private funds in time and that it would therefore require a "precautionary recapitalisation" - or rescue - by Italy.

The fate of MPS is critical for a number of reasons. It is Italy's third largest bank and a failure to secure the private funds would immediately raise doubts about the stability of a number of other Italian banks, such as UniCredit, which also need to raise private capital.

Any rescue of the institution by Italy under EU rules could lead to billions of euros in losses for retail investors, which in turn would damage the ruling Democratic party at a time when it has already been diminished by Matteo Renzi's resignation as prime minister last week following his defeat in a referendum on constitutional reforms.

Under new EU rules, taxpayer funds cannot be used to rescue a bank unless bondholders take losses first.

Italy could probably get the green light from Brussels to compensate certain junior bondholders, lessening the damage to investors and the political fallout, but the details of any such agreement are far from clear.

Analysts said any such arrangement would involve refunding investors who fall below certain thresholds in terms of income and wealth.

Shares in MPS closed down 10% on Friday following reports of the ECB's decision. The ECB refused to comment and gave no formal confirmation to MPS, but its decision may have closed the door to a private-sector solution under which major investors, including the sovereign wealth fund of Qatar, would invest €5bn in cash.

Federico Santi, an analyst at Eurasia Group, said that state support would likely be forthcoming if the private-sector solution failed to materialise.

Santi said any amount of "burden sharing" or losses inflicted on junior bondholders would be hugely unpopular and a serious blow to the government. He said that it might nevertheless be easier for an incoming government led by the prime minister-designate, Paolo Gentiloni, to take unpopular measures, since Renzi would still want to lead his party into elections. A new poll is expected to be called early next year.

Lorenzo Codogno, chief economist at LC Macro Advisors, said: "Now that the political situation is about to stabilise and a government will be in office on Tuesday, the solution for MPS could equally be in sight, but it is still not clear whether a private solution is still feasible or, more likely, some public money would be necessary.

"The problems of Italian banks will continue to drag on for months, if not years, but at least a framework would be in place to address the most pressing issues. It is now the final countdown."

The country's third-largest lender has already been bailed out twice in modern Italian history, but it became clear after Britain's vote to exit the EU, which sent shockwaves across financial markets, that the Siena bank would require a third bailout.

The bank's financial problems are nothing new. Italian banks have been weighed down by €360bn of non-performing loans that were mostly taken out by small Italian businesses which have been battered by years of recession. Italy returned to growth in 2015, but the improvements are only modest and the International Monetary Fund predicted that GDP would not likely return to pre-crisis levels until the mid-2020s.

MPS's issues were exacerbated by other mistakes - principally a poorly judged €9bn acquisition - but its primary issue is that billions of euros in loans were extended by the bank at a time when the scale of the impending recession was being underestimated.