In a statement released yesterday, Walton said he and his wife felt compelled to contact Brian Cowen after details of the skit appeared in newspapers and television reports.
“From what I have heard and read so far the stories are of concern to myself, my wife and also my children as they have seen reports on You Tube,” Walton said in a statement.
“As a result, we felt the best thing at this point was to write to An Taoiseach ourselves to get more details and the exact context of the various stories.”
The statement said Walton, who holed the winning putt in the 1995 Ryder Cup, felt “anger” at this week’s events.
Walton’s letter will heap further pressure on Mr Cowen who was forced to apologise on Wednesday for performing badly on a morning radio interview just hours after he finished partying at his parliamentary party’s annual conference.
Mr Cowen has repeatedly denied he was drunk or hungover on the radio show. The controversy, labelled “garglegate” by some, has raised questions over his leadership just as Ireland seeks to convince investors it is not on the brink of a debt crisis.
A renowned mimic, Mr Cowen is reported to have regaled the media and political colleagues, including senior government ministers, with a song and impersonations, including one of Walton.