Federer is one of the few who have spoken to Woods since the golf star's Nov. 27 car accident and subsequent firestorm over extramarital affairs.
Although the 28-year-old Swiss, who has won 15 Grand Slam singles titles, admits only to "just following it from afar."
"All I can say, I'm not going to talk about his personal life," top-ranked Federer said Saturday, replying to a question from The Associated Press, "but I wish him all the best getting back, hopefully on the golf course, resolving his problems, and see how he goes.
"That's about it."
Federer and Woods are among the world's most recognizable sports stars and a friendship between them has evolved -- they've even appeared together on TV advertisements.
Much of the criticism of Woods in the wake of the scandal has pointed to his diminished status as a role model.
Federer said he doesn't feel any pressure to stay squeaky clean.
"I just try to be myself, not change for the press or the public or the fans," he said. "If they like me, that's great. If they don't, that's too bad."
He said it was most important to him that he upheld the principles of fair play, respect for the game and his rivals and to be polite to people he meets.
"Those are key things my parents have taught me," he said. "You know, I try to do the same thing.
"Sure, I'm doing a lot of press conferences, and not being able to hide on the tennis court is not an easy thing sometimes," he added. "But I think I've done well over the years."
In an interview published Friday by French sports daily L'Equipe, Federer said he'd expressed his support to Woods in a telephone call, and predicted Woods will be back soon "as the wonderful golfer we know."
He said that Woods' car accident in November and subsequent reports about his private life have been hard on the golfer and his family.
"The tabloids are going crazy, sponsor contracts are falling apart ... I've always been aware that the image you patiently construct for an entire career can be ruined in a minute," Federer was quoted as saying. "It scares you a bit, but that's the way things are."
Woods hasn't been seen in public since the accident, and other friends have said they have tried -- unsuccessfully -- to reach him.
"Tiger needs calm. And soon he'll become the wonderful golfer that we know again," Federer was quoted as saying.