Williams has been the regular caddie for Woods since 1999
Tiger Woods has distanced himself from comments made by his caddie, Steve Williams, who said he had no respect for Phil Mickelson.
On Saturday, Williams was reported as saying that he hated Mickelson and that Woods did not get on with him either.
But Woods said on Monday: "I was disappointed to read the comments about Phil, a player I respect. The matter has been discussed and dealt with."
Mickelson's management said Williams's comments were "grossly inaccurate".
New Zealander Williams, who has caddied for Woods since 1999, was originally quoted by the Taranaki Daily News saying he "hated" Mickelson, adding: "I wouldn't call Mickelson a great player."
He later confirmed the quotes were accurate, adding: "I was simply honest and said they (Mickelson and Woods) don't get along.
"Mickelson pays me no respect at all and hence I don't pay him any respect. It's no secret we don't get along either."
Mickelson hit back immediately, saying: "After seeing Steve Williams's comments, all I could think of was how lucky I am to have a class act like Bones (Jim Mackay) on my bag and representing me."
Woods and fellow American Mickelson, the world number three, have been US Ryder Cup team-mates five times.
I worked with Tiger for 10 years and I can tell you he wouldn't have been very happy with that
Phil Mickelson's coach
Mickelson's coach, Butch Harmon, said he was "shocked" by Williams's outburst.
"I can't believe he said what he said. I think it's deplorable he would say something like that," said the American, who has also coached Woods.
"Golf is a game of honour and integrity and that was a very uncalled for remark. I don't think it's any reflection of what Tiger thinks of Phil Mickelson."
Harmon said he could not understand why Williams lashed out.
"Phil Mickelson is one of the most popular players in the world, every bit as popular as Tiger Woods," he said.
"He's a nice guy, all the guys like Phil, so I don't know where Steve was coming from with that comment. Personally, I would assume he would wish he'd never made it.
"I would have loved to have heard a recording of the conversation between (Williams) and Tiger. I worked with Tiger for 10 years and I can tell you he wouldn't have been very happy with that."