Nathan Lewin, a lawyer for the Jewish group Chabad, said in a statement provided to The Associated Press that Chabad was the rightful owner and Putin's proposal was not acceptable.
"The collection must be returned to the Agudas Chasidei Chabad library at Chabad's worldwide headquarters in Brooklyn, New York," Lewin said.
Chief Judge Royce Lamberth of the US District Court here last month fined Russia $50,000 a day until it returns the documents to Chabad.
On Tuesday, at a meeting of government officials at the Jewish Museum and Tolerance Center in Moscow, Putin floated the idea of transferring them to the museum as a way to resolve the impasse. He said all the sides in the dispute should "strive not to inflame the situation but search for a solution," The New York Times reported.
Russian news agencies reported that Putin criticized Lamberth's ruling, saying "discussion of this problem has taken on elements of confrontation." Russia claims the collections are state property.
Last month, the Russian Foreign Ministry called the ruling "an absolutely unlawful and provocative decision" and threatened a tough response if US authorities try to seize Russian property in an attempt to get the fines.
Russia had earlier halted all art exhibit loans to the US, fearing they would be seized and held hostage in the court battle. That's despite Chabad's assurance in court filings that it will not go after any art deemed culturally significant by the State Department – which is the case for major exhibitions. Such art is already protected from legal claims under the Immunity from Seizure Act.
There are two collections at issue: Some 12,000 religious books and manuscripts seized during the Bolshevik revolution and the Russian Civil War nearly a century ago; and 25,000 pages of handwritten teachings and other writings of religious leaders stolen by Nazi Germany during World War II, then transferred by the Soviet Red Army as war booty to the Russian State Military Archive.
The books and manuscripts, some hundreds of years old, record Chabad's core teachings and traditions.
The case has been dragging on for eight years, and efforts to get the materials returned date back decades, involving presidential administrations and members of Congress of both parties.
Lamberth concluded earlier that the records are unlawfully held by the Russian State Library and the Russian military archive, and in 2010, he ordered the Russian government to turn them over to the US Embassy in Moscow or to Chabad's representative. But Russia refused, leading to the fines, which Russia hasn't paid.
The Obama administration unsuccessfully urged Lamberth not to issue the fines, arguing they wouldn't help resolve the dispute, would be counterproductive and would hurt US foreign policy interests.
The Russian embassy in Washington did not immediately respond to a request for comment Thursday.