BMPS, the world's oldest bank and Italy's third-biggest, launched a bid to sell fresh shares this week under plans to raise five billion euros ($5.2 billion) to shore up its capital base.
The result of the share offer is expected by Friday but the bank acknowledged late on Wednesday that it had failed to attract an anchor investor after pinning its hopes on a big Qatari take-up.
A separate debt-for-equity swap offer, which is also part of the plan to replenish its coffers, reaped just over two billion euros, the bank said.
The plan additionally entails selling off 27.6 billion euros in bad loans. The European Central Bank has given the bank until December 31st to fund its recovery or risk being wound down.
The Italian government has, however, said it stands ready to step in if necessary. The bank had the worst results in a July stress test by the European Banking Authority and admitted this week to having just four months' liquidity left.
BMPS is at the centre of a crisis in Italy's banking sector - made up of some 700 banks - which is buckling under the weight of bad loans estimated to total 360 billion euros.
The bank's stock lost another 7.5 percent in Milan on Thursday, closing at 15.08 euros.
This took its drop since the start of the year to a staggering 87 percent.
'833 euros per family'
But investors still hoped that the crisis will end with some kind of viable solution, including a possible rescue by the government.
"A state bailout would at least allow the lender to continue as a going concern," said David Cheetham at XTB.
The Italian parliament approved on Wednesday a 20-billion-euro bailout package that would aim to stem the woes of the ailing banking sector.
"This is like forcing every family to pay 833 euros to save banks in trouble," quipped Codacons, a consumer rights group.
Analysts say the poor appetite among private investors so far towards bolstering the bank's coffers by five billion euros raises the likelihood of a state injection.
"The low probability of achieving this amount increases (the) odds of some kind of government rescue," Ipek Ozkardeskaya, of London Capital Group, said in a note to clients.
But the Italian government is hamstrung by recent EU rules requiring the pain of a rescue to be shared by investors, so that taxpayers are not left footing the bill as has often been the case since the financial crisis.
But such burden-sharing - rather than an outright bailout - worries the Italian government because many of BMPS's bonds are held by some 40,000 small shareholders whose anger could become political dynamite.
Last year's rescue of four small banks led to heavy losses for small savers, prompting demonstrations and at least one suicide - not a scenario the government wants to see repeated.
Rome now has several options depending on how much the bank manages to raise itself, said economist Lorenzo Codogno, of LC Macro Advisors Limited and a former senior Italian finance ministry official.
"If the shortfall is limited, the government could step in and inject probably up to another billion" without triggering burden-sharing rules.
But, he added that "if the whole operation fails, the government would have to intervene" with a "precautionary recapitalization".
This means shareholders and holders of junior bonds, a risky class of debt, must contribute to saving the bank.
If it comes to that, the government may seek ways to compensate high-street savers for their losses in some form that is acceptable to EU regulators.
Finance Minister Carlo Padoan on Wednesday said that the Italian banking system "is solid, even if there are some crisis situations" and insisted that the 20 billion euros set aside was "sufficient".
Founded in Siena in 1472, BMPS has been in trouble for years.
Weakened by the disastrous purchase in 2007 of the Antonveneta bank at twice the estimated value, it quickly drifted into scandal when its management team was accused of fraud and misuse of funds.
It subsequently ran up huge losses and has had to raise capital twice since 2014.