The warning comes as negotiations over the release of the last 7.2 billion euros ($8.1 billion) in rescue funds from Greece's massive bailout from the International Monetary Fund, European Union and European Central Bank are deadlocked, with payment deadlines looming.
All eyes are on a meeting of the 19 eurozone countries to take place Thursday in Luxembourg.
Deepening the tensions, Greek Prime Minister Alexis Tsipras said Wednesday an EU "fixation" on pension cuts would scupper any hopes of a default-saving agreement.
"There is no room for further cuts without affecting the core of the (pension) system," Tsipras said after meeting with visiting Austrian Chancellor Werner Feymann, one of the few European leaders supporting Greece in the talks.
"This insistence on cutting pensions is incomprehensible," the Greek premier said. "If Europe insists on this incomprehensible fixation ... it must accept the cost of a development that will benefit no one in Europe."
In one of the starkest warnings so far from a Greek institution, the Bank of Greece said failure to reach an agreement would " mark the beginning of a painful course that would lead initially to a Greek default and ultimately to the country's exit from the euro area and -- most likely -- from the European Union."
Yet while the atmosphere between Greece and its creditors has deteriorated, the Bank of Greece insisted that only a "little ground" separated the two sides.
Relations between Bank of Greece governor Yiannis Stournaras and the ruling radical left Syriza party have been strained from the start, with the leftists trying to block his appointment last June.
Analysts have long warned that a default could set off a chain of events leading to a messy exit from the eurozone.
Tsipras said Wednesday that his government had gone as far as it could in meeting the demands of the creditors for tax hikes and pension reform in return for bailout funds.
"Our proposals fully safeguard the fiscal targets the institutions set for 2015-2016," he said.
He said he was prepared to shoulder the political cost of a deal in Greece's parliament -- providing it was an "honest compromise".
"If we do not (get an honest deal), it is us again who will say the great 'no' to continuing a disastrous policy," he added.
The head of the eurozone countries, Jeroen Dijsselbloem, said Wednesday he was still working to keep Greece within the fold and dismissed any predictions about a so-called Grexit as premature.
Greece is due to make a 1.6 billion euro payment to the IMF at the end of the month, with another 6.7 billion euros due to the ECB in July and August -- payments that Greek officials say they cannot afford.
With his creditors saying his reform proposals are insufficient, Tsipras on Tuesday accused creditors of trying to "humiliate" his country.
Elected on an anti-austerity platform in January, Tsipras has been reluctant to accept any further cuts.
European Commission head Jean-Claude Juncker hit back by accusing Tsipras of misleading Greek voters.
"The debate in Greece and outside Greece would be easier if the Greek government would tell exactly what the Commission... are really proposing," Juncker said.
Polls show most Greeks support the government's negotiating strategy, though the approval rating has steadily fallen in recent months.
On Wednesday evening, demonstrations are planned in Athens and other cities to protest the creditor demands for further cuts.
A union close to the ruling Syriza party unfurled banners from the balcony of the EU offices in Athens.
"The people cannot be blackmailed, the country isn't for sale," the banner read.
Deal is 'historical imperative'
The Bank of Greece said that if the country left the 19-strong group of countries using the euro it would lead to a deep recession, dramatic declines in incomes and a spike in unemployment in the southern European nation.
"This is why the Bank of Greece firmly believes that striking an agreement with our partners is a historical imperative that we cannot afford to ignore," it said.
"From all the evidence available so far, it seems that a compromise has been reached on the main conditions attached to this agreement and that little ground remains to be covered."
When it comes to the terms of a potential new deal on the bailout, the Bank of Greece backed the government's position that after years of austerity and the worsening of its economy Greece needs further time to pay back the billions it borrowed.
In particular it raised the politically sensitive subject of relief on the country's debt, which is now mostly held by Greece's European partners as the bailout funds have been in loans.
Greek leaders of all political colours have never forgotten the prospect, raised three years ago by eurozone ministers, that in return for reform Greece could have some of its debts written off.
But it appears extremely unlikely that Greece's eurozone partners will return to this idea any time soon as it would face likely fierce political opposition in a number of countries, especially Germany.