The Minister for Arts, Sport and Tourism, Mr O'Donoghue, has asked the board of the Hunt Museum in Limerick to examine claims by the Simon Wiesenthal Centre that some of its collection may have been looted by the Nazis.
Mr O'Donoghue said he had received the letter containing the claims which the centre sent to the President, Mrs McAleese. He sent the letter to the museum, whose collection was amassed by the late John Hunt and his late wife, Gertrude.
The centre has claimed that the couple had "intimate business relationships with notorious dealers in art looted by the Nazis" and it has called for an independent inquiry into the collection.
However, Mr O'Donoghue said he wanted to hear the board's response before deciding on the next course of action. "I want to progress this as quickly and methodically as possible. I'm not doing anything until I hear from them," he said.
Mr O'Donoghue will also write this week to the Paris-based international liaison director of the Wiesenthal organisation, Dr Shimon Samuels.
No date has yet been fixed for a meeting this week of the museum board, which has never previously investigated any possible links between the Hunt collection and the Nazis.
This is despite commissioning a report in the form of an essay in 1998 which found that John and Gertrude Hunt "fitted seamlessly" into a post-war art market coloured by "wide-scale Nazi thefts".
In addition, the board never responded to an article last year in the Irish Arts Review about a guide published by the museum, which referred to the "Nazi associations" of the Hunts.
The article was written by Erin Gibbons, an archaeologist and museum consultant, who was then co-researching a book on the Hunts.
Her article also said: "The professional activities of the Hunts in the world of antiques have cast a long and uncomfortable shadow over this collection, but this is never referred to."
A subsequent edition of the Irish Arts Review carried a response to the piece, which was signed by Ms Mairead Dunleavy, a former director of the museum who then had no involvement with the museum. With the Government seeking a response to the Wiesenthal centre's allegations from the board, it is now expected that the failure to investigate previous allegations will be raised at the meeting this week.
Board members include the head of the University of Limerick, Dr Roger Downer, who is deputy chairman. Others include business figures in Limerick such as Mr Tony Brazil, Mr Niall Greene, Mr Cian O'Carroll, and Ms Maria O'Gorman Skelly.
In addition, the directors include the adoptive children of the Hunts - Mr John Hunt jnr and Ms Trudi Hunt - who reject the allegations made by the Wiesenthal organisation.
Mr John Hunt jnr and Ms Trudi Hunt received €761,000 in tax relief for a donation to the museum they made in 1999.
The donation was designated for tax exemption under Section 1003 of the 1997 Taxes Consolidation Act by a selection committee.