DUBLIN — Ireland has formally applied for a bailout from the European Union and the International Monetary Fund, Brian Lenihan, the country’s finance minister, said Sunday.

Speaking on Ireland’s RTE radio, Mr. Lenihan said the application would be approved at a cabinet meeting later Sunday in Dublin.

The bailout would be in the tens of billions of euros, he said, adding that the final figure was subject to further negotiations. Analysts and politicians have suggested that the size of the package may well approach €80 billion, or $109 billion.

Perhaps €15 billion would be set aside in a fund to support the country’s troubled banks, which have been hemorrhaging deposits. Another €60 billion or so would be allocated to Ireland itself so as to give it the flexibility of staying out of the bond markets.

Prime Minister Brian Cowen said Saturday that borrowing at 8 percent was “prohibitive” for Ireland, so it seems likely that the government will follow Greece’s approach and secure a bailout package that would free the country from dependance on the bond markets.

The Irish cabinet began meeting at 3 p.m. Sunday and was expected to make an announcement at 7 p.m.

What remains unclear are what kind of conditions the I.M.F. and the Europe Union would impose on Ireland in exchange for a bailout. Mr. Cowen has already said Ireland was already putting an adequate budget-cutting plan in place, but given the size of the bailout being discussed, it would be surprising if E.U. and I.M.F. officials did not demand more cuts, accompanied by tax increases.

“There will be a lot of pain for the taxpayer and a lot of people will lose their jobs,” said Michael Noonan, the chief economic spokesman for Fine Gael, the main opposition party.

In particular, analysts and opposition politicians say that the fear is that unless some aid package from Europe and the International Monetary Fund was put forward soon, an already worrying erosion of bank deposits might become more serious.

According to data from the Irish Central Bank and the European Central Bank, the six troubled Irish banks have markedly increased their reliance on outside funds in order to compensate for a wave of deposit withdrawals that have picked in the last week

E.C.B. data shows that €130 billion in outside funding have been funneled to Irish banks, with €95 billion being directed to the large locally based banks. These banks are now wholly dependent on Europe for their survival, running up loan-to-deposit ratios that now exceed 160 percent, above and beyond prudential banking guidelines guaranteed payday loans.

On Nov. 12, the Bank of Ireland reported that its outside borrowings had increased by €12 billion, or 11 percent of its assets. And on Nov. 19, Allied Irish Bank reported that its extra borrowings were €27 billion, or 16 percent of its balance sheet.

Barclays Capital estimates that €28 billion in extra funding is going to Anglo Irish, the troubled real estate lender that has chalked up more than €30 billion in failed loans.

Anglo Irish has been fully nationalized and the government has pinned the blame for much of Ireland’s troubles on it. Evidence now that deposit flight is gaining speed at Allied Irish and Bank of Ireland comes as another blow to the Irish authorities and has made the banks a higher priority than finalizing the government’s four-year budget plan.

People who have been briefed on the discussions now say that the bank problem will be the main issue for discussion at the cabinet meeting Sunday, and that the executives of the Irish banks have been told to stand ready in case extraordinary actions are taken.

What a bank rescue plan would look like is unclear.

Prime Minister Brian Cowen said Saturday that some form of a contingency fund was likely. Now, it would seem that the main aim of the fund would be to either sink further amounts of capital into the banks. A more radical option would involve forced mergers, a “fire sale” of one or more banks to an outside investor, or both.

Some analysts feel that the extent of the bank losses has been overstated. Goldman Sachs issued a much remarked upon report last week which said that NAMA, the government body responsible for buying the band loans from the Irish banks, had overestimated their losses.

“That is the first time anyone has said that,” said John Fitzgerald, an economist at the Economic and Social Research Institute in Dublin.

All the same, as the negotiations continue, Dubliners, who are now well into the country’s third consecutive year of negative economic growth, are calling for some form of action to restore calm.

“If I had a lump sum of money now, I would be very nervous about putting it in an Irish bank,” said Brian Kavanagh a 60-year-old cab driver. “There is just no confidence in the banking sector here.”

Stephen Castle contributed reporting from London.

Ireland Asks for Aid From Europe, Minister Says