DUBLIN (Reuters) - Permanent tsb (>> Permanent tsb Group Holdings PLC) will launch the first public share sale by an Irish bank since the financial crisis on Tuesday with a 400 million euro (288.7 million pounds) offering, a source close to the matter said, in a key test of investor appetite for the sector.

The sale by the smallest of Ireland's three domestically owned banks and the only one to fail European stress tests last year is part of its plan to raise 525 million euros to help fill a capital hole identified by the European Central Bank (ECB).

The 99.2 percent state-owned bank last week secured shareholder approval to raise up to 400 million euros in equity, but did not specify whether it would use a public or private sale. The money will be used to repay a government loan.

Permanent tsb (PSTB) will raise the remaining 125 million euros through so-called additional tier 1 bonds. It would be the first Irish bank to sell such bonds, which are regarded as more risky by investors as they convert into equity or are written down if a bank's capital falls below a certain level.

A spokesman for the bank, whose shares were delisted from the main Dublin and London stock exchanges following a 4 billion euro government bailout in 2011, declined to comment on the share sale plans.

A public offering would give the bank a wider investor base and allow retail investors to get involved, but it risks a public failure if demand evaporates.

PSTB's holding company is listed on Ireland's junior market but the public offering would mark the bank's return to a full listing.

The share sale will be watched closely by the country's No. 2 lender Allied Irish Banks (AIB) (>> Allied Irish Banks PLC), which has appointed Goldman Sachs (>> Goldman Sachs Group Inc) to advise on a possible stake sale during the next 12 months.

Shares in No. 1 lender Bank of Ireland (>> Bank of Ireland) have more than tripled in value since the government sold 35 percent in a private placement in 2011 but unlike its two larger rivals, PSTB is still loss-making.

Lauded in the immediate aftermath of the financial crisis as the only Irish bank to avoid a state bailout due to its lack of exposure to commercial property developers, PSTB was effectively nationalised in 2011 mainly due to its high proportion of loss-making mortgages that track the ECB's low interest rate.

These "tracker mortgages" contributed to a 48 million euro loss before tax last year down from a 668 million loss in 2013. PSTB expects to return to profit by the end of 2016.

The government is keen to partially recoup its investment in PSTB ahead of an election next year and local media has said Dublin may try to raise 300 million euros through an additional share sale. PSTB has declined to comment on the report.

The government, which also owns AIB, has said it wants to retain a majority stake in PSTB.

There has been a run of lenders floating in Britain where investors have been keen to buy into the economic recovery there and PSTB is hoping Ireland's status as the fastest growing economy in the European Union will attract investors.

(Editing by Carmel Crimmins and Mark Potter)

By Graham Fahy and Conor Humphries