Story highlights The three missing Afghan officers are in custody at U.S.-Canada border

They are now being questioned by federal authorities

This is the second incident in which Afghan soldiers went missing in the United States

Three Afghan National Army officers -- guests of the U.S. military at a training exercise in Massachusetts -- disappeared on Saturday and reappeared Monday in the custody of Canadian border guards.

The men are in custody at the Rainbow Bridge, a checkpoint on the border at Niagara Falls, and are being interviewed by federal authorities, Massachusetts State Police David Procopio said.

The military, State Department and other government agencies are remaining especially quiet about the choice the three Afghan officers made to go off the radar.

Maj. Jan Mohammad Arash, Cpt. Mohammad Nasir Askarzada and Cpt. Noorullah Aminyar went missing Saturday after a trip to a mall. The three were reported missing by base security late Saturday and were last seen at a Cape Cod mall in Hyannis.

Authorities said they posed no threat to the public.

Shelbe Benson-Fuller, regional press officer at U.S. Customs and Border Protection, said the agency was notified by the Canadian Border Services Agency when the men were taken into custody.

Canadian officials declined to confirm if the three officers were seeking asylum.

Arash, Askarzada and Aminyar arrived in the United States on September 11 for the annual Exercise Regional Cooperation and were quartered at Joint Base Cape Cod, the Massachusetts National Guard said.

Their disappearance comes in the wake of an incident earlier this month when two Afghan police officers training with the DEA went missing for six days.

Mohd Naweed Samimi, 24, and Mohammad Yasin Ataye, 22, were training in Quantico, Virginia, and went missing on September 13. They were later found on September 18 in Buffalo, New York, according to DEA spokesman Rusty Payne.

The men, who Payne said were monitored by escorts at all times, never posed any threat or danger. They wanted to stay in the United States, but authorities found them and sent them home.

In both cases, the Afghan attendees at the training sessions were cleared and given visas by the State Department.

A source familiar with the process told CNN that officers are usually handpicked and vetted, including a complete background check, possible polygraph and interviews to determine whether they are a flight risk.

The source says that the three officers did not break the law.

The Massachusetts State Police concurred.

The Exercise Regional Cooperation, in which the three soldiers training in Cape Cod were participating, included troops from six nations. Despite their disappearance, the guard said the exercise has continued.

The purpose of the exercise is to train participating nations in "stability operations" and "operations conducted during United Nations mandated peacekeeping operations," according to the guard.

Roughly a dozen Afghan soldiers are still participating.

The Regional Cooperation exercise has been conducted annually since 2004, according to the Massachusetts National Guard. Tajikistan is the lead nation for conducting the exercise this year. The last exercise was held in 2013 and led by the Republic of Kazakhstan's Ministry of Defense.

Gen. Zahir Azimi, a spokesman for the Afghan Defense Ministry, told CNN that the ministry is investigating both incidents.