The M23 rebel movement that ravaged the eastern Democratic Republic of Congo is all but finished as a military threat, a senior UN envoy said Monday, diplomats said.

"Practically all M23 positions were abandoned yesterday, except a for small triangle at the Rwandan border," Martin Kobler told the UN Security Council by video-link, according to diplomats.

Kobler, the civilian special representative in charge of the UN stabilization mission in the DRC, was speaking after Congolese government forces backed by UN troops carried out an offensive.

Troops from the UN peacekeeping mission MONUSCO have a mandate to conduct operations against rebels in the region of Goma, capital of the restive province of North Kivu.

A Tanzanian UN soldier was killed in the fighting, but the rebels were rolled back and local civilians are overjoyed, Kobler said, according to officials present at the closed door meeting.

He said that the M23 had abandoned a key position on Mount Hehu near the Rwandan border, reportedly adding: "It is practically the military end of the M23."

The mainly Tutsi M23 movement emerged in April 2012 after a mutiny by former rebels who had been taken into the Democratic Republic of Congo army under a 2009 deal.

Rebels accused Kinshasa of failing to keep the terms of that deal, then on-off talks in the Ugandan capital Kampala failed after the government refused to give an amnesty to about 80 rebel leaders.

The M23's numbers were limited, but the movement, which allegedly received support from neighboring Rwanda, was seen as a threat to stability in a region with long history of conflict.