Seizures cannot be good for the Asian antiquity market. But it is not clear what impact they are having this week on sales, gallery owners said. Many collectors are savvy and familiar with widespread reports about Subhash Kapoor, a former Manhattan dealer who is accused of having run the largest antiques smuggling operation ever uncovered in the United States.

Mr. Kapoor primarily dealt in objects from South Asia — India, Pakistan and Afghanistan in particular — and those are the sorts of items that have been seized in the past week by agents from Immigration and Customs Enforcement’s Homeland Security Investigations. There have been fewer reported instances of stolen antiquities from Japan, China or Korea turning up in the United States.

“Historically, Asian governments haven’t monitored their antiquities in the same way” as nations like Italy, Greece, Turkey, and Egypt, said Leila A. Amineddoleh, the former director of the Lawyers’ Committee for Cultural Heritage Preservation. “It makes them vulnerable.”

Mr. Kapoor, who is awaiting trial in India, has been the pivotal figure in Operation Hidden Idol, and the sheer volume of illicit artifacts he is said to have donated or sold — hundreds are in museums around the world — has raised questions about the level of scrutiny being practiced in both the art market and the museum world. Museums in the United States, Australia and Singapore, among others, have returned items obtained from Mr. Kapoor, many valued at well above $1 million. The Antiquities Coalition, which fights illicit antiquities trafficking, said major dealers and auction houses have the resources to conduct due diligence and should coordinate more with law enforcement and source countries.

“The burden of proof should fall on these global businesses,” said Deborah M. Lehr, the coalition’s founder, “not on the individuals and countries who are victims of the illicit trade, to validate antiquities before any sale.”

Some experts say many problems would be solved if law enforcement shared information about suspect items rather than publicized eye-grabbing confiscations. The Committee for Cultural Policy, an advocacy group for collectors, has called for a digital system under which museums and collectors could document items publicly and address foreign claims in a neutral forum.