Australia Monday flatly rejected comments from Afghan President Hamid Karzai that a recent night-time raid which left two men dead was carried out without the approval of local authorities.

Kabul had slammed Australia over the mission, carried out in the wake of last week's killing of three Australian troops by a rogue Afghan soldier, describing it as a "unilateral military operation".

"The president condemns the operation as a breach of the Memorandum of Understanding signed between Afghanistan and NATO on the special military operations," Karzai's office said in a statement.

But Defence Minister Stephen Smith said the operation in restive Uruzgan province had full authorisation, was conducted jointly with 60 Australians and 80 Afghan troops, and had followed the established rules of engagement.

"The statement that has been issued by President Karzai's palace over the weekend in Kabul that this operation was not authorised is wrong," Smith said.

"That is not factually correct, and this point has been made strongly by Australia's ambassador to Afghanistan to palace and presidential officials."

Smith said Australia was "disappointed" by Karzai's comments, describing the situation as a "misunderstanding".

The operation, which was authorised by the governor and police chief of Uruzgan where some 1,500 Australian troops are based, was aimed at capturing the Afghan accused of killing the three Australian soldiers, he said.

He said two insurgents had been killed and a third detained during the raid.

The man in custody was suspected of having helped or sought to help the Afghan soldier, Hekmatullah, flee after he allegedly gunned down three Australian troops last week.

"The outcome of the operation has been the detention of an individual who is regarded not just as a leader of the insurgency in Uruzgan province but a person who has also sought to or actually assisted Hekmatullah in his escape," Smith told reporters.

The insider attack -- of which there have been more than 30 against foreign troops this year -- prompted US special forces in Afghanistan to suspend training for about 1,000 Afghan police recruits to vet existing members.

Smith said Australian and international forces were still "in pursuit" of Hekmatullah and they had come to no conclusion about his motive.

"It's either a personal dispute, a cultural difference or a genuine insider effected by the Taliban," Smith said of previous cases.

"The Taliban claim all of them as you would expect; there is evidence of a small number of incidents where infiltration has occurred."