NATO expressed regret on Sunday over air strikes that killed 24 Pakistani soldiers as the United States sought to repair relations with Islamabad, plunged into fresh crisis over the lethal attack.

Pakistan reacted with fury over the killings of two dozen soldiers, widely interpreted in the local media as a "deliberate" assault by NATO helicopters and fighter jets on two military posts on the Afghan border early Saturday.

Islamabad conveyed its anger to the United States, blocked NATO convoys from crossing into Afghanistan, ordered a review of its alliance with the US and mulled whether to boycott a key conference on Afghanistan next month.

Hundreds of enraged Pakistanis took to the streets, burning an effigy of President Barack Obama and setting fire to US flags across the country of 167 million where opposition to the government's US alliance is rampant.

At the largest rally, attended by 700 people outside the US consulate in the port city of Karachi, protestors shouted: "Stay away Americans, Pakistan is ours, we stand shoulder-to-shoulder with our army".

The United States, which depends on Pakistan as a vital lifeline to supply 130,000 foreign troops fighting in landlocked Afghanistan, on Sunday scrambled to salvage the alliance, backing a full inquiry and expressing condolences.

NATO also sought to soothe Islamabad's rage, but stopped short of issuing a full apology to Pakistan for the "tragic, unintended" killings.

A Western official said allies were trying to ascertain "exactly" what Pakistan's public position meant and to prevent lasting damage as a result of the suspended supply lines into Afghanistan.

It also remains unclear exactly what happened in the early hours of Saturday in Pakistan's tribal district of Mohmand.

Investigators are to examine whether Afghan and American troops along the border may have been fired upon first -- whether by insurgents or soldiers -- and to what extent their operation was coordinated with Pakistan.

NATO secretary general Anders Fogh Rasmussen issued a statement, saying he had written to Pakistani Prime Minister Yousuf Raza Gilani.

"I have written... 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. "This was a tragic unintended incident."

Pakistani Foreign Minister Hina Rabbani Khar earlier telephoned US Secretary of State Hillary Clinton to convey a "deep sense of rage" as a joint funeral was held for the dead soldiers, their coffins draped in the national flag.

Khar said attacks on military outposts were "totally unacceptable", contravened international law and violated Pakistani sovereignty.

She spoke to Clinton to inform her of Pakistan's response, formulated at an emergency meeting of cabinet ministers and military chiefs, saying that Pakistan was forced "to revisit the terms of engagement".

Pakistan said its attendance at a conference of more than 90 delegations due in Germany on December 5 was "being examined", although a boycott is considered unlikely given how much Pakistan stands to lose by not attending.

US Secretary of Defense Leon Panetta and Clinton offered their "deepest condolences" and backed "NATO's intention to investigate immediately".

They stressed the importance of the US-Pakistani partnership and pledged to remain in close contact with Pakistan "through this challenging time".

But a top US senator warned that there were strings attached to the billions of dollars in US aid to Pakistan each year, urging greater co-operation.

"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 co-operation with us," Republican senator Jon Kyl said on the Fox News Sunday talk show.

Senator Dick Durbin, a top Democrat, offered condolences but said US soldiers were caught in a "diplomatic morass between the incompetence and corruption in Afghanistan, and complicity in parts of Pakistan".

Pakistan's army chief Ashfaq Kayani, who had hosted the US commander in Afghanistan for talks on coordination only one day before the attack, led the mourners in funeral prayers in the northwestern city of Peshawar.

In September 2010, Pakistan also shut the main land route for NATO supplies at Torkham for 11 days after accusing NATO of killing three Pakistani troops.

The border was reopened after the United States formally apologised and most commentators expect the latest crisis to be resolved in a similar way.

The fact that Pakistan also ordered the United States to leave the Shamsi air base, reportedly used as a hub for US drone strikes on militants, was also interpreted as a sign of Islamabad's relatively limited options.

Pakistan has made similar demands in the past and there have been reports that American personnel already left the secretive base, southwest of Islamabad, earlier this year.

NATO troops frequently carry out operations against Taliban insurgents close to the border with Pakistan, which in many places is unmarked, as Pakistani troops also wrestle with putting down a homegrown Taliban insurgency.

Afghan and US officials have frequently accused Pakistani troops at worst of colluding with the Taliban or at best of standing by while insurgents fire across the border, often in clear sight of Pakistani border posts.