Diplomats said on Monday that NATO chief George Robertson would contact UN Secretary General Kofi Annan to confirm the organisation's willingness to extend the International Security Assistance Force (ISAF).
The 5300-strong force, which has been led by NATO since August, is currently confined to Kabul.
Beyond the Afghan capital, lawlessness reigns in large parts of the Central Asian country.
The decision was taken by the so-called silence procedure, under which NATO states had been given until 10:00 (07:00 GMT) to lodge any objections to the agreement.
The silence was not broken, and therefore agreement was confirmed.
A NATO official said the decision was twofold - agreement for Germany to take command of a "Provincial Reconstruction Team" (PRT) in Kunduz, and agreement "in principle to the expansion of the ISAF mission beyond Kabul".
The Taliban are regrouping in
ISAF has been deployed in Kabul since December 2001. It was set up weeks after the defeat of the Taliban to control the capital.
Twenty months on, Afghanistan's provinces are troubled by in-fighting between rival commanders and an intensified insurgency by fighters loyal to the Taliban.
One of the scenarios under consideration at NATO is to send between 2000 and 10,000 troops to other Afghan cities, and to multiply the number of "Provincial Reconstruction Teams" (PRTs) already active in several regions.
The PRTs were set up under the leadership of the United States, whose troops are engaged in a separate hunt for al-Qaida and Taliban fighters, as a means of extending the Western security blanket to zones outside Kabul.