The report, by a renowned American nuclear scientist, said the operation highlighted the importance of China as a transit point for Iran's nuclear program, and called for sanctions against any Chinese firms involved.
The Institute for Science and International Security (ISIS) report said an Iranian front company used a Chinese commercial website to try to acquire 100,000 ring-shaped magnets, which it is banned from importing under United Nations sanctions, in late 2011.
Two magnets were needed for each of 50,000 first-generation centrifuges used to enrich uranium at Iran's nuclear plants, in a process that Western powers say is designed to build nuclear weapons, a charge Tehran denies.
The ISIS report by US scientist David Albright suggested that the operation meant that Iran was trying to "greatly expand" its number of first-generation centrifuges even as it builds more advanced machines.
"China needs to do more to show that it is a responsible member of the global economy," the report said.
"In particular, it should crack down on the efforts of Iranian smuggling networks."
The ISIS said it could not establish whether Iran found a Chinese supplier willing to provide the ring magnets.
The Washington Post, which first reported the ISIS report, quoted a European diplomat with access to intelligence as saying Iran was positioning itself to make swift progress on its nuclear program.
"Each step forward makes the situation potentially more dangerous," the unnamed diplomat was quoted as saying.
The White House would not comment explicitly on the ISIS report but said that it was aware of Iran's "aggressive" efforts to avert UN sanctions.
"The unprecedented international sanctions put in place against Iran are not only designed to crystallize the choice for the Iranian regime regarding its nuclear program, but also to deter and disrupt Iranian procurement of components to support its nuclear program," White House spokesman Josh Earnest said.
The report will raise new concerns about the extent of progress in Iran's nuclear program, despite international sanctions, which will be at the top of the agenda when President Barack Obama visits Israel next month.
Israeli Prime Minister Benjamin Netanyahu said Monday that Iran was now closer to crossing the "red line" after which it would be able to build a nuclear weapon but had not yet reached that stage.
It will also raise the stakes for the latest round of talks between world powers and Tehran, due to take place in two weeks.