Thursday's move was passed unanimously as reports of clashes between Nkunda's Tutsi rebels and pro-government fighters threatened a ceasefire deal that has seen hundreds of rebels pull back from frontline positions.
The rebel decision raised hopes for peace talks that could end the violence, but Joseph Kabila, the DR Congo president, has so far refused to meet Nkunda.
"We are asking for talks and maybe if Kabila can accept it will be the end of the war," Nkunda said.
Kabila will, however, discuss the conflict with Jose Eduardo dos Santos, his Angolan counterpart, on Friday.
The Angolan military, which backed the Kinshasa government in DR Congo's 1998-2003 war, but has repeatedly said it will not interfere in this conflict.
More UN troops
The UN peacekeeping mission in the DRC, known as Monuc, is the UN's largest and the reinforcements will bring it to about 20,000 troops and police.
"It's important that there's a Monuc peacekeeping force with the capacity to oversee the implementation of a political framework"
UK ambassador to UN
John Sawers, the UK's ambassador to the UN in New York, told Al Jazeera that the new UN force would be deployed as fast as possible.
"Certainly, we will want to help countries that are ready to deploy, we want to try to assist them as best we can in getting troops on the ground rapidly," he said.
"It's important that there's a Monuc peacekeeping force with the capacity to oversee the implementation of a political framework. How long it will be, we're not sure, but this is a matter of urgency."
Lieutenant Colonel Jean-Paul Dietrich, the Monuc spokesman, welcome the Security Council decision.
"It will give us some capability to react much faster to any major crisis," he said.
About 5,000 UN troops are currently in North Kivu province where fighting flared at the end of August.
"The means we have are fine for patrolling, but to do more than that we are already stretched. What we do not have is a mobile reserve to act quickly when an event happens," Dietrich said.
He said the extra peacekeepers would help the UN provide a humanitarian corridor to protect the hundreds of thousands of people displaced by the fighting.
Nkunda has repeatedly accused the government of backing the Rwanda Hutu fighters, some of whom - according to Rwanda - took part in the 1994 genocide of Tutsis in their country.