WASHINGTON — The abduction of more than 200 schoolgirls in Nigeria has led to new scrutiny of the United States’ counterterrorism strategy toward Boko Haram during Hillary Rodham Clinton’s tenure as secretary of state.

At the heart of the issue is a debate carried out within the Obama administration on whether it was time to officially designate the group as a “foreign terrorist organization.”

Republican lawmakers assert that the delay in making that designation shows that Mrs. Clinton was not firm enough in dealing with Boko Haram. But some former officials say that the issue is being politicized because of Mrs. Clinton’s status as a likely presidential candidate.

The debate took place in 2011 and 2012 amid mounting concern about the group’s attacks.

The Justice Department, the F.B.I., American intelligence officials and counterterrorism officials in the State Department favored the designation because of Boko Haram’s role in the growing violence in Nigeria and because of intelligence reports that some of its members had links to Al Qaeda in the Islamic Maghreb.