But the full extent of extra resources coming from the military alliance remains unclear.
Germany, along with France, had both said this week that they would wait until after a London conference on Afghanistan on January 28 to decide on further action.
According to French officials, the US has asked Germany to provide 2,000 more troops, France and Italy 1,500 each and Britain 1,000.
A handful of media reports in recent weeks have said that the German government was already considering an increase of around this size.
Karl Lamers, a defence expert with Germany's governing Christian Democrats, said on Thursday that the new mandate could be altered at a later date if necessary.
"If there is a new situation after the Afghanistan conference, a new political assessment after the talks in London about goals and expectations of the Afghan government and the allies, then we will adjust the mandate accordingly," he told public broadcaster Deutschland radio.
Italy's government has approved sending 1,000 extra soldiers to Afghanistan next year, the defence and foreign ministers announced on Thursday.
In addition to Italy, Britain, Georgia, Poland and Slovakia have all promised increased troop deployments but other countries such as France and Denmark appear more cautious.
The US now has 71,000 troops in Afghanistan, while other Nato members and allies collectively have 38,000 service members there.
With the added reinforcements, the international forces will grow to more than 140,000 soldiers.