Massachusetts state police were notified that the three were being questioned by federal authorities at Rainbow Bridge, which connects Niagara Falls, New York, and Niagara Falls, Ontario, said spokesman David Procopio, who did not have further details.
There was no immediate comment from the Pentagon. US Customs and Border Protection officials in Niagara Falls said they didn't have the men in custody.
Messages left for Canada Border Services Agency weren't immediately returned.
They arrived at Camp Edwards on Sept. 11 and were last seen Saturday at the Cape Cod Mall in Hyannis during an off day.
The soldiers were reported missing by base security personnel Saturday night. They were identified as Maj. Jan Mohammad Arash, Capt. Mohammad Nasir Askarzada and Capt. Noorullah Aminyar.
Gov Deval Patrick, who had been briefed over the weekend on the situation, said earlier today that the military did not believe the three soldiers posed a danger to the public.
"There is a lot of speculation within the military that they may be trying to defect," he said. Army Col Steve Warren, a Pentagon spokesman, said earlier that 14 Afghans taking part in the Cape Cod military exercise were "thoroughly vetted" prior to coming to the US, so officials do not believe they are a threat.
The Regional Cooperation training exercises have been held annually since 2004 to promote cooperation and interoperability among forces, build functional capacity, practice peacekeeping operations and enhance readiness.
Procopio said state police considered it to be a missing persons case, because there was no information that any crimes had been committed.
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