The alliance has some 64,000 men in the country, and has been locked in bitter fighting with Taliban-led insurgents ahead of presidential elections Aug 20.
The mission is growing increasingly unpopular in many NATO states as losses mount.
Tensions with Russia are also set to occupy his tenure following last year's Russian invasion of NATO hopeful Georgia.
NATO froze ties with Russia after the war, but re-started formal cooperation in the spring. The sides remain at odds over issues such as NATO enlargement and missile defence.
On Thursday, Russia's ambassador to NATO, Dmitry Rogozin, said he wanted Rasmussen to give up the idea of taking Georgia and Ukraine into the alliance as a mark of 'respect' for Russia.
Rasmussen is to chair his first NATO meeting Tuesday when he meets the ambassadors of the alliance's 28 members.