Dispute over the Jewish books and documents claimed by the Chabad-Lubavitch group adds to tensions between Moscow and Washington, which have seen ties deteriorate over human rights and security issues since Putin's return to the Kremlin in May.
"The Schneerson Collection belongs to Russia," Putin said in a grand new Jewish museum in Moscow, in referring to texts held in Russian libraries and archives, some of them confiscated by the Soviet Union from Nazi forces during World War II.
A Washington judge in January ordered Russia to pay $50,000 a day in fines for failure to adhere to a 2010 ruling to return the collection, triggering angry reaction from Moscow, which called the decision "absolutely unlawful and provocative."
"If we now open a Pandora's box and start satisfying similar requests, there will be no end to these claims. Maybe one day we will be able to do this, but now we are absolutely not ready for this. This is impossible," Putin said.
Moscow bristles at what it sees as attempts to lecture it from abroad, especially by its Cold War-era foe Washington, and Russians are proud of the Soviet Union's victory over Nazi Germany in World War II.
The collection of Jewish texts has been the subject of a legal and diplomatic tug-of-war since before the Soviet Union collapsed in 1991.
Putin, a former KGB spy, said the texts could be put on display at the Jewish museum "as a gesture towards those people who really want to solve this problem and not use it as reason for emotions and confrontation."
Late last year Hungarian Jews asked Russia to return scrolls and valuable religious items looted by Nazis and later by the Red Army in World War II. At that time, Moscow did not comment on the claim backed by the Hungarian government.
Washington and Moscow recently have scrapped bilateral deals after Moscow was enraged by the US Magnitsky Act, named for an anti-graft lawyer who died in a Russian prison, banning visas of Russians deemed rights violators.
Moscow retaliated with its own blacklist of US officials. It also banned Americans from adopting Russian orphans and outlawed US-funded NGOs that it said meddled in political activities.