A painting by Lucian Freud, titled “Girl in Attic Doorway,” was sold to an anonymous buyer for $12 million at Art Basel, its seller, Acquavella Galleries, said today.

“We can’t go into who bought it,” the New York dealer’s owner, William Acquavella, said in an interview. “We’ve been sworn to secrecy,” he said, declining even to disclose the nationality of the buyer.

The canvas, dating from the mid-1990s, had been reserved during much of the fair’s preview yesterday. Russian billionaire Roman Abramovich had visited the Acquavella booth. Sheikh Saud Al-Thani, cousin of the Emir of Qatar, and the Hollywood actor Brad Pitt were also seen at the preview.

Art Basel is the world’s largest fair of modern and contemporary art. Sellers are hoping the rich remain as eager to spend money as they were at contemporary art auctions last month in New York. Those sales raised a record $971.5 million with fees as buyers from emerging markets shrugged off the credit crisis.

During the May sales, Mr. Freud became the world’s most expensive living artist at auction when his 1995 nude, “Benefits Supervisor Sleeping,” sold for $33.6 million with fees at Christie’s International in New York. The painting was bought by Mr. Abramovich, the Art Newspaper reported.

Acquavella is the worldwide agent of British artist Mr. Freud, according to the gallery’s entry in the Art Basel catalog.

The Zurich and London dealers Hauser & Wirth sold three new sculptures by American artist Paul McCarthy for $1.8 million each, the gallery director, Iwan Wirth, said.

“The opening of Art Basel is one of the few situations where dealers can re-create the competition of an auction,” Mr. Wirth said.

Mr. McCarthy’s 11-foot-high, brown-painted fiberglass sculpture, “Captain Ballsack,” had recently been completed in the artist’s studio in an edition of three. One sold to an unnamed European museum, the other two to American and European collectors, Mr. Wirth said.

“This is probably our best ever Art Basel,” Mr. Wirth said. “Although we’ve sold less to Americans, we’ve met a lot of new buyers.”

Mr. Wirth said the gallery also sold the 2008 Subodh Gupta triptych, “Still Steal Steel #4,” for $1 million, and the 34-inch-square Agnes Martin painting, “Untitled,” dating from 1960, for $3 million.

Other galleries were more reluctant to discuss sales. “We don’t like to discuss prices,” the director of the Zurich-based dealers Bischofberger, Tobias Mueller, said.

Mr. Mueller said a reserve had been placed on Vincent van Gogh’s 1887 oil-on-board view of rooftops through a window, “Vue de la Chambre de l’Artiste.” The painting last sold at auction in May 2007 when it fetched $5 million with fees at Christie’s International in New York, according to the saleroom result tracker Artnet.