ISLAMABAD, Pakistan — The top elected official in northwest Pakistan said Thursday the country should rethink its relationship with America after a U.S. airstrike that reportedly killed 11 Pakistani soldiers.

The U.S. and Pakistan remained at odds in their versions of a Tuesday night clash on the Afghan border that led to American planes dropping bombs on insurgents who had staged an attack inside Afghanistan.

President Bush's national security adviser said it was not clear exactly what happened and American officials "have not been able to corroborate" Pakistani troops died. The U.S. "would be very saddened" if that were true, Stephen Hadley told reporters traveling with Bush in Europe.

The incident is presenting a stiff test for an already-strained alliance, a partnership many here say has cost many Pakistani lives with limited recognition for their cooperation in the U.S. campaign against international extremist groups.

Haider Khan Hoti, chief minister of North West Frontier Province, a restive region next to Afghanistan where Islamic militants are strong, said the airstrike was "absolutely naked aggression."

"After condemnation, we should do some serious rethinking of the ties that we have, because on the one side in the war on terror we are expected to offer them cooperation and on the other hand our security forces are being targeted," Hoti said in Peshawar, the area's main city.

Some Pakistanis directed their anger over the airstrike at President Pervez Musharraf, who allied the country with the United States after the Sept. 11 terror attack.

In Peshawar, about 50 Islamic students brandished banners with slogans such as "America is the most terrorist country in the world" and "U.S. ally Musharraf, resign immediately."

A similar gathering in the southern city of Karachi carried a sign saying "Rulers and generals of Pakistan, give a tit-for-tat response to American missile attack."

In the Mohmand tribal area, where the disputed bombing occurred, tribal elder Malik Mazal Mahmood said Musharraf's "wrong policies" were to blame.

"If the Americans really consider themselves brave, then they should use ground forces, and if they do it, we will be happy to face them," he said. "Musharraf allowed Americans to kill our people, and now Americans have started killing the soldiers of Pakistan."

Others expressed satisfaction that the new government — led by opponents of Musharraf — had quickly protested the attack.

"Musharraf's government used to hide such things in the past, but the new government at least didn't do it, and rather it took a bold step by openly opposing and criticizing America," said Kawanar Sadique, a clerk at a garment factory near Lahore.

The border clash comes at an especially sensitive time.

Pakistan's government is negotiating with tribal elders trying to secure peace with militants along the Afghan border in hopes of curbing violence. It is a step back from the military offensives pursued by Musharraf.

Western officials fear the peace deals could give more space for Taliban and al-Qaida fighters to operate freely, but Pakistan insists the negotiations are not with terrorists but with Pakistani militants willing to lay down their arms.

Pakistan has called the airstrike "completely unprovoked and cowardly" and lodged a diplomatic protest. The Pentagon maintains it was a "legitimate strike" against militants who attacked U.S.-led coalition forces just over the border in Afghanistan.

On Thursday, the U.S.-led coalition in Afghanistan released video to support its account. The excerpts, however, do not show the Gorparai border post where Pakistan said its troops died, and one explosion occurs off screen without explanation.

The grainy, monochrome images show about a half-dozen men firing rifles and rocket-propelled grenades from a ridge at coalition troops off camera in the valley below. According to the voiceover, the ridge is in Afghanistan's Kunar province, about 200 yards from the Pakistan border and close to the checkpoint.

Neither the border post nor any other structures are visible in the video excerpts, which were shot by a surveillance drone circling above the mountainous battle zone.

The video shows "anti-Afghan militants" moving to a position identified as inside Pakistan and the impact of a bomb that the voiceover says killed two of them. The survivors fled into a ravine, where three more bombs fell. The voiceover said all the militants were killed.

U.S. officials have said about a dozen bombs were dropped in all.

Maj. Gen. Athar Abbas, spokesman for Pakistan's army, said the military was analyzing the coalition video and statements by U.S. officials. On Wednesday, he said all the Pakistani troops killed and injured were in bunkers and buildings destroyed by the airstrike. He said the soldiers had reported no nearby militant activity.

But he did say Afghan troops were attacked by insurgents before the airstrike was called in. An organization of Pakistani Taliban groups also said eight of its fighters were killed in the battle.