Matt Lauer, Wife Deny Split

Matt Lauer and his wife, Annette, are denying a tabloid report that they have split and that he has moved out of their home, calling the story a "work of fiction."

"I am living in my apartment with Annette and my children as a family and a couple," Lauer tells People. "I have never moved out. I am not moving out. There is no truth to that."

In a separate statement, Annette Lauer told People: "Out of self respect, I want to stand up for our family and protect them."

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In its new cover story, the National Enquirer reports that Lauer moved out of the family's New York City apartment two months ago after Annette accused him of cheating on her while he was covering the Winter Olympics in Vancouver. The report also says that Lauer partied almost every night during the Games, delayed his return home to continue partying, and missed Valentine's Day with his wife.

However, Lauer, 52, says that he was in bed by 7:30 p.m. most nights in order to wake up for Today's live broadcasts at 4 a.m. local time in Vancouver. Annette and their children — Jack, 8, Romy, 6, and Thijs, 3 — also flew to Vancouver to spend Valentine's Day together, and he returned home two days before Today wrapped up in Vancouver, he added.

"Have we had a completely perfect, easy marriage? No. But the stories you've read over the years are not true," Lauer said. "I don't think we're any different than any married couple that's been together for 12 years. The accusations [of infidelity] are ridiculous and I'm not going to [dignify] them with an answer. It's not true."

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The Enquirer is standing by its report, saying in a follow-up story that Annette's mother, Johanna Struijk, told its reporters that her daughter is doing fine in the wake of the split. The tabloid also says that its reporters have staked out the family's apartment and have not spotted Lauer leaving in the morning to go to work.

Calls to the Enquirer were not immediately returned.

Lauer, who's currently covering the Cannes Film Festival, and Annette, a Dutch-born model, briefly separated in 2006 while she was pregnant with Thijs. She filed for divorce, but the two later reconciled.