"Recently, members of an infiltration network affiliated to Britain have been arrested," an unnamed source told the Fars news agency, which is considered close to the powerful Revolutionary Guards.
The report named Edalat, a professor of computer science and mathematics at Imperial College in London.
Britain said earlier it was "urgently seeking information" from Iran following reports of the academic's arrest.
Edalat was detained on April 15, according to the New York-based Centre for Human Rights in Iran (CHRI).
He founded the Campaign Against Sanctions and Military Intervention in Iran, which describes itself as "an independent campaign organisation with the purpose of opposing sanctions, foreign state interference and military intervention in Iran".
CHRI said Edalat was arrested by the Revolutionary Guards and that he had refused to post bail on Wednesday, arguing that he was innocent and should be released unconditionally.
The group said Edalat's home in Tehran had been raided and his computer was confiscated, as well as CDs and notebooks.
"We are urgently seeking information from the Iranian authorities following reports of the arrest of a British-Iranian dual national," a Foreign Office spokeswoman said.
CHRI said 30 dual nationals have been arrested in Iran, primarily on spying charges, since the 2015 nuclear deal with world powers.
The most high-profile British case is that of Nazanin Zaghari-Ratcliffe, a Thomson Reuters Foundation employee who was arrested two years ago and is serving a five-year sentence for alleged sedition.
Another Imperial College scientist, Kaveh Madani, was forced to leave Iran and quit his job as deputy head of the government's environment agency earlier this month following pressure from hardliners.
He later said he had been placed under unauthorised surveillance from the moment he returned to Iran in September.
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