* Claims capture of towns of Kiwanja and Kalingera
* M23 rebels say they withdrew from Kiwanja
* Rebels threaten counter-offensive unless talks restart
By Kenny Katombe and Chrispin Mvano
KINSHASA, Oct 27 (Reuters) - The Congolese army said it had recaptured two more towns and was heading for the rebel stronghold of Rutshuru in a third day of fighting on Sunday, raising the prospect of a military victory by government forces.
A Congolese army officer on the front line said it had taken the towns of Kiwanja and Kalingera from the M23 rebels on Sunday, a day after wresting the strategic town of Kibumba near the Rwandan border from the insurgents.
Fighting was continuing at Kiguri, 25 km (15 miles) north of Goma, the biggest city in eastern Congo, he said.
The army had also opened a second front to the north of M23 positions and was moving southward to Rutshuru, officers said.
"We are consolidating the zones we have conquered," army spokesman Colonel Olivier Hamuli told Reuters near the front line. "Very soon we will take Rutshuru. Those who disarm we will accept, the others we will pursue."
M23 said in a statement on Sunday it had withdrawn its troops from Kiwanja, accusing the army of sending in fighters in civilian clothing in a bid to draw U.N. troops into the conflict.
M23 threatened to withdraw its delegation from stalled peace talks in the Ugandan capital Kampala unless there was an immediate end to hostilities. It said it would then launch a large-scale counter-offensive.
Following two months of relative calm, fighting flared up on Friday morning after talks broke down when M23 pressed for a full amnesty for its leaders. Each side blamed the other for starting the fighting.
Congolese President Joseph Kabila said unconditional amnesty was not an option and last week threatened a return to military action.
Congo's army, supported by a new United Nations intervention brigade, scored its first victories against the 20-month-old rebel movement in late August, forcing the rebels away from Goma.
The U.N. brigade has a tough new mandate to eliminate armed groups in the eastern provinces, though it has not been involved in the last three days of fighting.
The support of the brigade and the weakening of the rebels has fuelled belief that Congo's army - notoriously disorganized, undisciplined and under-supplied - could defeat M23.
Army sources told Reuters reporters in Goma that M23 had been weakened by desertions, with some 40 rebels taking advantage of a corridor created by the government troops to allow then to flee rebel lines.
M23 began in early 2012 as a mutiny by soldiers demanding the government implement the terms of a 2009 peace deal signed with a previous Rwanda-backed rebel group, many of whose members had been integrated into the army.
U.N. investigators and the Congolese government have accused Rwanda of supporting M23, charges Rwanda has repeatedly denied.
Hamuli said some M23 fighters had fled towards the Rwandan border in the face of the army advance.
"There are small pockets of M23 resistance in the hills near Rwanda," he said. "We think Rwanda has to prove its good faith and oblige M23 to disarm, or disarm them itself."
He refused to discuss the possibility of a return to peace talks in Kampala. "We are soldiers," he said. "We will continue to do our jobs as soldiers."