The NATO air strike triggered anti-US protests in Pakistan [AFP]

US President Barack Obama has told his Pakistani counterpart that last month's deadly NATO air strike on Pakistani territory was "not a deliberate attack", the White House said.

Obama offered his condolences "on the tragic loss" in a call to Asif Ali Zardari on Sunday

The November 26 raid killed 24 Pakistani troops along the border of Afghanistan and Pakistan and caused one of the most serious rifts between the two countries in recent years.

"The president made clear that this regrettable incident was not a deliberate attack on Pakistan and reiterated the United States’ strong commitment to a full investigation," the White House said in a statement.

"The two presidents reaffirmed their commitment to the US-Pakistan bilateral relationship, which is critical to the security of both nations, and they agreed to stay in close touch."

The incident sparked rage in Pakistan, where citizens are already angry over their government's perceived obeisance to US interests, especially the wide latitude given to US drone attacks and special operations inside the country.

In response, Pakistan has so far refused to take part in a US probe into the air strike. It has also shut down a vital NATO supply line into Afghanistan and ordered American personnel to leave Shamsi air base.

The base is widely understood to have been a hub for the covert CIA drone attacks on Taliban and al-Qaeda commanders in Pakistan's troubled border areas with Afghanistan.

US personnel have started leaving the base, a senior Pakistan Army official confirmed to Fox News on Sunday.

According to the official, US cargo planes arrived at the base to take equipment and other gear out of the country.

Also in the wake of the raid, Pakistan decided not to take part in the Bonn Conference in Germany on the future of Afghanistan that opens on Monday. The decision, together with the Taliban's boycott, has cast the event's usefulness into doubt as Pakistan's influence is seen as a major factor for stability in Afghanistan.