The British newspaper The Guardian reports Garcia was asked in jest while on stage at the European Tour's awards dinner Tuesday night if he would invite Woods to dinner during the U.S. Open.
The Guardian reports Garcia said: "We will have him round every night. We will serve fried chicken."
The newspaper says Garcia released a statement through the European Tour: "I apologise for any offence that may have been caused by my comment on stage during The European Tour Players' Awards dinner. I answered a question that was clearly made towards me as a joke with a silly remark, but in no way was the comment meant in a racist manner."
Garcia has acknowledged not getting along with Woods.
The verbal feuding between the two began May 11 during the third round of The Players Championship. It resumed this week on both sides of the Atlantic when Woods offered a one-word answer if he thought about contacting Garcia to put the matter to rest.
"No," he replied with a tight smile.
Garcia fired back at a sponsor function outside London.
"He called me a whiner. That's probably right," he told reporters. "It's also probably the first thing he's told you guys that's true in 15 years. I know what he is like. You guys are finding out."
Garcia tried to tone down the barbs Tuesday at the BMW Championship when asked about the spat.
"I can't like everybody and there's people that you connect with and there's people that you don't," Garcia said at Wentworth. "He doesn't need me in his life, I don't need him in mine and let's move on and keep doing what we're doing. There's never really been a true connection I would have with maybe Luke (Donald) or Adam Scott or some of the other guys that I get along with well.
"I think we should kind of move on and forget -- well, it will be difficult to forget -- but kind of move on about what happened."
Disputes among golfers are nothing new, though it's rare for two high-profile players to go at each other through the media.
The animosity between them goes as far back as 2000, when Garcia beat Woods in the Monday night exhibition "Battle at Bighorn" and celebrated as if he had won something much more important. Two years later in the U.S. Open at Bethpage Black, where Woods won wire-to-wire, Garcia complained that the second round should have been halted because of rain and that "if Tiger Woods would have been out there, it would have been called."
The latest chapter took place on the second fairway at the TPC Sawgrass in the third round, when Garcia had a one-shot lead. He was preparing to play his second shot on the par 5 from the fairway when he was disrupted by cheers from the gallery around Woods deep in the trees. Woods was about 50 yards away and couldn't see the Spaniard. The crowd burst into cheers when Woods took a 5-wood from his bag to play a risky shot through a gap in the trees.
During a storm delay, Garcia suggested in a TV interview that Woods could have kept the crowd from cheering if he had been paying closer attention. Later that evening, Woods said he understood from marshals that Garcia had already hit.
"Not real surprising that he's complaining about something," Woods added, which only fired up the Spaniard.
Garcia said the next day to Sky Sports, "He's not the nicest guy on tour."
Woods was at media day Monday for the AT&T National, where he is the defending champion, when he received the final question about Garcia and gave the one-word answer. Garcia offered a more detailed response when asked in England if he would ever call Woods.
"First of all, I don't have his number," Garcia said. "And secondly, I did nothing wrong and don't have anything to say to him. And he wouldn't pick up the phone, anyway."
Garcia conceded their dislike for each other has been "going on for a long time."
"The problem is, I'm one of the guys that has to say something," Garcia said. "A lot of people think about it, but don't want to say anything. He can and will beat me a lot of times, but is not going to step on me. I'm not afraid of him."