"There is a lot of diplomacy that has to occur and they need to understand that our support for them financially is dependent on their cooperation with us," Republican Senator Jon Kyl said on the Fox News Sunday talk show.

The air strikes Saturday have brought another chill to already frosty relations between the two uneasy allies, with Islamabad still a key partner for US military operations in neighboring Pakistan.

The United States, which depends on Pakistan as a vital life-line to supply 130,000 foreign troops fighting in landlocked Afghanistan, has scrambled to salvage the alliance.

In a joint statement, US Secretary of Defense Leon Panetta and Secretary of State Hillary Clinton have offered "deepest condolences" and said they backed "NATO's intention to investigate immediately."

Senator Dick Durbin, a top Democrat, echoed Clinton and Panetta's statement, offering condolences, but warned that the crisis would likely further endanger US troops in the region.

"As difficult as it is to find our way through this diplomatic morass, between the incompetence and corruption in Afghanistan, and complicity in parts of Pakistan, our soldiers are caught right in the middle of this at a time when they're trying to bring peace to this region," he said.

"I have written to the Prime Minister of Pakistan to make it clear that the deaths of Pakistani personnel are as unacceptable and deplorable as the deaths of Afghan and international personnel," he said in a statement.

"This was a tragic unintended incident."

"I offer my deepest condolences and sympathy to the families of the Pakistani officers and soldiers who lost their lives or were injured, and to the government and people of Pakistan, following the regrettable incident along the Afghan-Pakistani border," Rasmussen added.

Pakistan says two border posts were fired upon "unprovoked" in the early hours of Saturday in Pakistan's tribal Mohmand district.

An investigation of the incident is likely to ask whether Afghan and American troops on the Afghan side of the border were fired upon first -- whether by insurgents or Pakistani military.

Pakistan on Sunday conveyed its "rage" to the United States over cross-border NATO air strikes and ordered a full-scale review of its frosty alliance with Washington and the military bloc.

Pakistan represents a vital life-line to supply 130,000 foreign troops fighting in landlocked Afghanistan, and Rasmussen joined US efforts in a scramble to salvage the alliance.

"I fully support the ISAF investigation which is currently underway," he said of the International Security Assistance Force fighting the war and which includes non-NATO allies.

"We will determine what happened, and draw the right lessons," Rasmussen added.

"NATO remains strongly committed to work with Pakistan to improve cooperation to avoid such tragedies in the future."

Earlier Sunday, Foreign Minister Hina Rabbani Khar telephoned US Secretary of State Hillary Clinton and conveyed a "deep sense of rage" as the military organised a joint funeral for the 24 troops who died.