The provocative painting seemed like an authentic work by Andy Warhol, depicting a nude man and woman gazing at each other with colorful shading around their bodies.

But the piece was a well-disguised counterfeit, among more than 200 fakes of works by artists like Banksy, Picasso and the Native American painter Fritz Scholder, which sold for a total of more than $2 million. Many of the works were made by an artist in Poland, and commissioned by a father and daughter living in New Jersey.

On Tuesday, the father and daughter, Erwin Bankowski and Karolina Bankowska, pleaded guilty in Federal District Court in Brooklyn to running a scheme to sell the counterfeit works.

The duo “painted themselves as purveyors of fine art while selling lies on canvas to unsuspecting collectors,” Joseph Nocella Jr., the U.S. attorney in Brooklyn, said in a statement.

Federal guidelines call for a prison sentence of 33 to 41 months for each defendant. Both Mr. Bankowski and Mr. Bankowska are citizens of Poland and face deportation after serving their sentences. They are set to be sentenced on Aug. 5.

Todd Spodek, a lawyer for Ms. Bankowska, 26, said his client had accepted responsibility for her crimes. Jeffrey Chabrowe, a lawyer for Mr. Bankowski, 50, said his client also accepted responsibility and had “made a terrible decision to support his family.”

Counterfeit art schemes date back thousands of years. Many forgers in recent decades have pulled off their operations by faking a work’s provenance, or documented ownership history, which elite art collectors check to determine authenticity.

Famous art forgers include Wolfgang Beltracchi, a German man who says he painted in the style of more than 100 artists, and Mark Landis, who has donated numerous fakes to dozens of museums. Two art forgery rings in Thunder Bay, Ontario, manufactured thousands of fake paintings presented as works by Norval Morrisseau, one of Canada’s most celebrated Indigenous artists.

Mr. Bankowski and Ms. Bankowska went to great lengths to conceal their efforts. In addition to creating the fake provenances, sometimes by using forged stamps from art galleries, they told buyers that the pieces were from art galleries that had since closed, prosecutors said. That made it harder for buyers to verify that the pieces were real.

The pair’s collection included splotchy pieces, often with strong political overtones, that were sold to reputable galleries and auction houses around the United States. One fake of a work by Banksy, the anonymous British street artist, that protested the Iraq War sold for $2,000. A knockoff of a painting by Raimonds Staprans, a Latvian American visual artist who died in January, sold for $60,000.

Mr. Bankowski and Ms. Bankowska also sold works that they claimed were made by Native American artists, earning a rarely used federal charge: the misrepresentation of Indian goods and services. One of the counterfeits was a fake of a landscape by Richard Mayhew, a painter of Black and Native American heritage; it sold for $160,000, prosecutors said.

Mr. Spodek, who has represented many people accused of elaborate scams, said his clients had taken great care to ensure the knockoffs looked authentic. He said the replicas that the father and daughter commissioned were “identical” to the originals.

“It’s not just selling on eBay,” Mr. Spodek said.