SYDNEY (Reuters) - Peter McGrath will continue as Australian Rugby Union (ARU) chairman following an investigation into an incident at the World Cup in France, the ARU said on Friday.

McGrath was alleged to have turned up drunk to an official function the day before Australia's quarter-final defeat by England in Marseille, leading to a formal complaint from one of the team's major sponsors.

The ARU said that although it would be counselling McGrath in relation to his behaviour, it retained confidence in his chairmanship.

"The allegation was thoroughly investigated and the board considered the results of that investigation and submissions by Mr McGrath," acting chairman Peter Cosgrove said in a statement.

"The Board believes this matter has been handled appropriately, and it is now closed."

McGrath stood down as chairman while the incident was investigated.

"This has been a very stressful time for me and my family," McGrath said.

"That said, ARU is committed to standards on and off the field and I understand the importance of the reputation of the ARU and its commercial partners.

"Rugby has been part of my life for many years and I now look forward to helping shape it into the future."