The US commander in Afghanistan on Saturday promised a full investigation after Pakistan said a NATO air strike killed at least 23 soldiers, sending his condolences over any troops who may have died.

"This incident has my highest personal attention and my commitment to thoroughly investigate it to determine the facts," said General John Allen, commander of NATO's International Security Assistance Force (ISAF).

"My most sincere and personal heartfelt condolences go out to the families and loved ones of any members of Pakistan security forces who may have been killed or injured," he added in a statement.

In the six months since US commandos killed Osama bin Laden near the Pakistani capital Islamabad without prior warning, Pakistani and US and Afghan officials have traded increasing complaints about cross-border attacks.

ISAF said Saturday it remained "committed to improving security relations" with Pakistan, including the coordination of operations along the border -- in many places unmarked -- "in our united fight against terrorism".

US ambassador to Pakistan, Cameron Munter, also express regret and reiterated promises of an investigation.

"I regret the loss of life of any Pakistani servicemen and pledge that the United States will work closely with Pakistan to investigate this incident," he said in a short statement released by the American embassy.

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

The border was reopened after the United States formally apologised.