PALM BEACH GARDENS, United States (AFP) - Northern Ireland star Rory McIlroy remains undecided about whether he would play for Ireland or Britain at the 2016 Rio de Janeiro Olympics, when golf returns to the Games programme.

For the first time since 1904, golfers will compete for Olympic gold but that brings the tricky question of nationality into play because Northern Ireland does not field its own team.

"I haven't made a decision yet," McIlroy told the US PGA Tour website on Wednesday. "There's no real urgency at the moment, and I couldn't even imagine planning my schedule that far ahead. I will have to decide, however, and take into consideration many sensibilities."

Another Northern Ireland golf star, Graeme McDowell, played for Ireland at last year's World Cup of Golf. That locked him into representing Ireland at Rio in 2016.

"It's a very touchy subject," McDowell said at the event. "You are going to end up upsetting someone."

McIlroy, a two-time major champion, plays this week at the US$6 million (S$7.6 million) US PGA Honda Classic, which he won in 2012 to secure the world number one ranking for the first time in his career.

But last year, McIlroy walked off the course in the middle of his second round, citing a toothache and mental fatigue, what he called his lowest moment of the 2013 season.

"I made a mistake walking off the course and disappointed not just myself," McIlroy said. "What's important, though, is that I have learned from that episode. I need to stay patient and play my way through the difficult patches."