By Stephen M. Silverman
Updated December 15, 2003 01:00 PM

Oprah Winfrey may rightfully consider herself the butt of David Letterman’s jokes, but the two TV powerhouses appear to be reaching some sort of rapprochement

On Friday, a spokeswoman for “The Oprah Winfrey Show” confirmed to Reuters that the media queen, 49, had turned the tables on CBS’s “Late Show” host by inviting Letterman to make his first-ever appearance on her program.

All last week, Letterman has been playfully goading Winfrey to join him on the air for an “hour of healing” in the wake of her quotes to Time magazine in which she vowed never to go on his show again after two previous guest stints.

“I felt completely uncomfortable sitting in that chair,” Winfrey said in Time. “But I have a great deal of respect for his talent.”

Starting last Monday, Letterman, 56, devoted part of his monologues to pushing Winfrey to come on his show so they could patch up their differences in a “Super Bowl of Love” officiated by self-help guru Dr. Phil McGraw (himself a frequent butt of Letterman’s jokes, though Dr. Phil did show up on “Late Show” earlier this year — and boosted Dave’s ratings.)

Only Oprah ignored Dave’s invites — until the end of the week.

At the taping of his show on Friday, Letterman announced, “Oprah no longer hates me,” and that she had invited him to appear on her show. Not that he RSVP’d.

“It can’t possibly happen because that would screw up the Super Bowl of Love,” Letterman said. “Because here’s what would happen: I would go on the Oprah show and I would break down and sob like a little girl.”

Letterman petulantly insisted Oprah must come on his show. “Dr. Phil will come out first and straighten me out because the problem is me,” he said. “I have an attitude problem. There is something wrong with me. And then, when he feels it’s safe, Oprah will come out. … And then the love will explode.”

Stay tuned.