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The appeal came from heads of state of the central African Great Lakes region who fear that if left unchecked the offensive by the M23 rebels could drag the volatile, ethnically-diverse and mineral-rich region back into another bloody conflict.
A statement signed by the regional leaders meeting in the Ugandan capital Kampala urged the M23 to abandon its threat to overthrow the elected government in Kinshasa and to "stop all war activities and withdraw from Goma".
It proposed deploying a joint force at Goma airport comprising of a company of neutral African troops, a company of the Congolese army (FARDC) and a company of the M23.
The leaders told M23 "to withdraw from current positions to not less than 20km from Goma town within two days", but did not say what the consequences would be if the rebels did not comply.
The rebel M23 movement, which has announced it intends to "liberate" all of Congo and march on the capital Kinshasa 1000 miles to the west, said it was still waiting to hear back from its political representative who was in Kampala.
But it expressed initial scepticism about a proposed joint deployment in Goma that included government troops returning.
"Will the population accept that? I doubt it. The population sees that M23 has changed things. With the (Congolese army) it was just harassment," M23 military spokesman Vianney Kazarama told Reuters.
Regional and international leaders are scrambling to halt the fighting in eastern Congo, fuelled by a mix of local and regional politics, ethnic rifts and competition for large reserves of gold, tin and coltan. The region has suffered multiple uprisings and invasions over the last 20 years.
The meeting in Kampala brought together Congo's President Joseph Kabila and the heads of state of Uganda, Kenya and Tanzania.
But Rwandan President Paul Kagame, who has vehemently denied accusations by Congo and U.N. experts that his government is supplying, supporting and directing the M23 rebellion, did not attend the summit, although he sent his foreign minister.
As the regional leaders met in Uganda, the Congolese government army reinforced its positions southwest of rebel-held Goma, in what appeared to be a move to block any further advance by the insurgents, who have routed Congolese army forces backed by United Nations peacekeepers.
The Great Lakes heads of state also proposed that U.N. peacekeepers present in and around Goma should provide security in a neutral zone between Goma and the new areas seized by M23.
They said police that were disarmed in Goma by the rebels should also be re-armed so they can resume working.
GOMA SITUATION "A MESS"
In the Congolese capital Kinshasa, authorities banned protests, citing the need to keep order in what national police chief Charles Bisengimana called a "undeclared state of war".
Goma was calm on Saturday, but UK-based international charity Oxfam said the city's resources were being strained by the influx of more than 100,000 people displaced by the recent fighting, many of them taking shelter in schools and churches.
"The Goma situation is a mess .. we've just got the green light to set up another camp, because all the other sites are full already," Tariq Riebl, Oxfam's humanitarian programme coordinator, told Reuters.
Riebl said M23 was allowing Oxfam to operate.
"The main thing is access, and we have that. They (the rebels) are not al Shabaab or the Taliban," he said.
Goma has been a regional HQ for the U.N. peacekeeping mission in Congo, known as MONUSCO, which has a 17,000 strong force across the huge country. MONUSCO is tasked with assisting government troops keep the peace and protect civilians.
MONUSCO has faced criticism inside and outside Congo for not doing enough to halt the rebels when the Congolese army fled Goma, but U.N. officials have argued it is not the mandate of the U.N. peacekeepers to directly engage the insurgents.
U.N. helicopter gunships fired at the rebels but were unable to beat them back at Goma, U.N. officials said.
Congolese government troops attempted a counter-offensive against the advancing rebels this week but were forced to pull back to the town of Minova on Lake Kivu, leaving a trail of soldiers' bodies and abandoned equipment in their wake.
"We are going to defend Minova, but we'll also try to push back the rebels," Congo army (FARDC) spokesman Olivier Hamuli said. Reinforcements were on their way to the front, he said.
M23 forces moved south through the hills towards Minova, in a strategic position on the road to Bukavu, the capital of South Kivu province. The rebels have said that Bukavu is their next objective and have vowed to sweep across the vast nation to Kinshasa if Kabila does not agree to talks.
Kabila, who has said he is willing to hear the rebels' grievances, appointed a new interim head of ground forces late on Friday.
General Francois Olenga Tete takes over from former army boss General Gabriel Amisi, who was suspended on Thursday over charges he had sold arms to other eastern rebels.
A MONUSCO spokesperson in Goma said around 10 women were raped in Minova by retreating Congolese soldiers.
The Congolese army, FARDC, said some soldiers had been arrested and sent to Bukavu for looting and extortion, but it denied there had been rapes.