WASHINGTON — The evidence of ties between the man accused of being the Times Square bomber and Pakistani militants has intensified debate inside the Obama administration about expanding America’s military presence in Pakistan, with some officials making the case to increase the number of Special Operations troops working with Pakistani forces in the country’s western mountains.

The American military presence in Pakistan has already grown substantially over the past year, and now totals more than two hundred troops, part of a program to share intelligence with Pakistani Army and paramilitary troops and train them to battle militant groups.

But the failed bombing in Times Square, and evidence that the accused man, Faisal Shahzad, received training in a camp run by the Pakistani Taliban, has given support to those who want to expand the mission.

In particular, some inside the administration believe that the C.I.A. program of killing militants from the air is insufficient for preventing attacks on the West, and that an expanded training mission might raise confidence in Pakistan’s military enough to launch an offensive in the militant sanctuary of North Waziristan, in the tribal areas.