"Obviously it would be a small fraction of the presence that we have today, but I think we’re willing to do that"

US Defense Secretary Robert Gates, who is on a surprise visit to Afghanistan, told US occupation troops on Monday that the American military should stay in the conflict-riddled country despite the rising human costs.

"Obviously it would be a small fraction of the presence that we have today, but I think we're willing to do that," AP quoted Gates as saying in a speech before a group of US troops at Bagram air field, which is the headquarters for US-led forces in eastern Afghanistan.

The Pentagon chief flew into Kabul on Monday to assess the US-led war amid tensions with Afghan President Hamid Karzai over the increasing number of civilian deaths in the country.

"The civilian casualties are a main cause of worsening the relationship between Afghanistan and the US," a statement from the Afghan presidency quoted Karzai as saying on Sunday.

Gates also plans to hold talks with Karzai as well as top US commander General David Petraeus.

Karzai rejected Washington's apology over the incident, calling on NATO to do more to prevent such incidents during airstrikes. The children were killed in a NATO helicopter raid while collecting firewood in the northeastern province of Kunar.

Hundreds of Afghans rallied on Sunday in capital Kabul to condemn civilian killings by foreign troops.