Separately, five Senate Democrats, including Dianne Feinstein of California, chairwoman of the Intelligence Committee, sent a letter to Defense Secretary Robert M. Gates and Secretary of State Hillary Rodham Clinton on Tuesday urging them to re-evaluate security aid to Pakistan.

Despite the anger on both sides, the Americans would like to maintain Pakistani cooperation as they try to wind down the war in Afghanistan, and Pakistan would like to keep aid flowing from the United States, which has amounted to more than $20 billion in the past decade.

When asked at Tuesday’s hearing about the impact of suspending aid to Pakistan, Gen. James L. Jones, President Obama’s former national security adviser, warned, “I would counsel against what might be a very tempting thing to do, but it might have long-term consequences that we would then have to deal with.”

American officials fear the exchange of fire on Tuesday will provide yet another irritant for both sides. NATO officials could not immediately confirm whether the helicopters had indeed entered Pakistan’s airspace, but said they were looking into the episode, which took place at Admi Kot Post in the North Waziristan tribal region of Pakistan.

An American military official said the Pakistanis were injured by a rock slide, not gunfire.

Pakistani military officials said the NATO helicopters came about 400 yards into Pakistani territory. The Pakistani Army “lodged a strong protest and demanded a flag meeting,” it said in a statement, referring to a meeting between officials from Pakistan and NATO on the border.

Last September, Pakistan shut down the land route through Pakistan that NATO uses to supply its forces in Afghanistan for more than a week after two Pakistani paramilitary soldiers were killed in a similar border clash.

However galling the current clash may be to Pakistani military officials, it was not clear that they would take similar action this time, as both sides may also be seeking to pull relations back from the brink.