U.S. Secretary of State Condoleezza Rice and her British counterpart David Miliband paid a surprise visit to Afghanistan on Thursday amid increasing insurgency and rift among the NATO member states over alliance mission in the country, according to an Afghan official who refused to be named.

Afghan officials are tight lipped over the visit of the two dignitaries due to security concerns but saying that they will call on President Hamid Karzai in the afternoon.

Rice and her British counterpart before holding meeting with President Hamid Karzai flew to Taliban's birthplace Kandahar to visit NATO's troops over there.

Rice who earlier visited London and exchanged views with British leaders over NATO mission in Afghanistan called for more support to Afghanistan.

The U.S. Secretary of State stressed in London that NATO's strategy should be shifted from keeping peace to fighting terror and hunting down insurgents, said the official.

Pentagon's Chief Robert Gates asked Washington's allies to contribute more troops to bolster NATO mission in Afghanistan not long ago.

Gates also announced deploying additional 3,000 troops in the war-torn nation this year.

However, Germany rebuffed to the call and stressed it had no plan to deploy troops in Afghanistan's troubled southern provinces where Taliban militants are active.

A major ally of the U.S.-led war on terror in Afghanistan Canada also linked extending mission to Afghanistan saying it would not extend mission beyond this year unless the NATO member states contribute more troops.

More than 55,000 troops from the NATO-led International Security Assistance Force (ISAF) and the U.S.-led Coalition have been fighting with Taliban and al-Qaida allies to ensure stability in Afghanistan.