WASHINGTON – The FBI arrested 10 Russian secret agents on June 27 after learning weeks before that one of them, Donald Heathfield of Cambridge, Mass., would soon be traveling abroad with a college-age son and might not return, a U.S. law enforcement official said Monday.

Heathfield’s planned departure was, in the official’s words, the big catalyst in deciding to take down a spy network that had been under surveillance by the FBI for more than a decade.

The official said Heathfield, whose real name is Andrey Bezrukov, was to have started late last month.

The FBI had reason to believe Heathfield might not be coming back, said the official, who spoke about the matter on condition of anonymity because the official was not authorized by the government to discuss it.

Two White House officials said Friday it became clear in early June that at least two of the Russians were making plans to leave the U.S.

The officials did not identify the two, but the law enforcement official said one of them was Heathfield.

According to one of the two criminal complaints in the case, another of the Russian agents, Anna Chapman, was planning to leave in mid-July for Moscow.

The FBI spent weeks preparing a 37-page complaint that a federal magistrate signed June 25, two days before the arrests.