But it reports far slower progress in disarming rival factions elsewhere in the north.
UN spokesman for Afghanistan Manoel de Almeida e Silva said that more than 6,000 small arms and 30 tanks had been collected in Kunduz since 10 November.
"Although there still remains several commanders in the region who need to be disarmed, the security situation has reportedly been improved since the beginning of the weapons collection," he said.
Only a few hundred weapons, however, have been collected in the volatile areas to the north, which are under the control of rival Uzbek commander Abdul Rashid Dostum and Tajik commander Ustad Atta Mohammad.
Both men swear allegiance to Afghan President Hamid Karzai, but recent fighting in areas under their control have underlined the fragility of the Kabul government's grip on the country.
Stability
The UN disarmament programme targets people who are not registered with the central Defence Ministry.
Mr Almeido e Silva said that over the past week both commanders Dostum and Atta had led a drive to disarm fighters in Samagna province and to the south-west of Mazar-e-Sharif.
So far they had collected 663 light and heavy arms, he said.
Disarmament programmes are also under way in Baghlan, Badakhshan and Takhar provinces but figures are not yet available for these areas.
One of the biggest challenges facing Hamid Karzai is to build a national army.
The mandate of the International Security Assistance Force (Isaf) was extended for a further year on Wednesday.
As well as assisting the Afghan Government to maintain security, Isaf is engaged in building up the Afghan army and police forces.