* M23 rebels tapping into local frustrations for support
* Government says Rwanda created the insurgency
* Country roiled by decades of minerals-driven conflict
By Jonny Hogg
GOMA, Nov 21 (Reuters) - When the shooting stopped in Goma this week, stunned residents watched with a mix of hope and despair as rebel conquerors paraded through the eastern Congolese city's streets and asked them to join the revolution.
"The M23 rebels say they want to bring change," a teacher who gave his name only as Peter said as fighters walked past in green fatigues, greeted by small groups of supporters. "But we don't need to hear it, we need to see it."
As rebels mount the most serious threat to the government of the Democratic Republic of Congo in years, a parallel struggle looms over whether M23 is, as it represents itself, a truly home-grown protest movement, or a foreign invasion by Rwanda keen to control the remote region's minerals resources.
The answer is as important as military might in determining whether the President Joseph Kabila's rule survives the insurgency, whose leaders threaten to cross the 1,000 miles of hills and jungle from Rwanda's border to his capital Kinshasa.
If defined as a popular uprising, M23 has a chance of winning over broad local support against a government that has seen its popularity plummet thanks to the slow pace of reform, rampant insecurity and widespread poverty.
But defined as a proxy force for Rwanda - the small but militarily tough neighbour that has intervened in Congo repeatedly over the past 18 years - it will likely be halted under intense international pressure.
Prior to taking Goma on Tuesday, rebels had sought to draw Kabila into talks along with other opposition figures and human rights organisations to address popular complaints; Kabila refused, saying he will talk only with Rwanda.
Since Goma's fall, and with other towns under threat, Kabila has said he will look into M23's grievances.
"By making this demand, M23 aimed to reduce the crisis to a domestic affair, thereby preventing Kinshasa from internationalising it," the risk consultancy International Crisis Group said in a research note.
Kabila's government has repeatedly referred to the rebellion as a Rwandan creation - a point of view backed by U.N. experts, who say Rwanda hands out orders to M23's commanders and provides soldiers and weapons to bolster its force.
Rwanda vehemently denies the claims.
Efforts by M23 to win over wider Congolese support have gone much further than calling for broad talks with Kabila.
Seeking to tap into local frustrations, M23 has set up an administration in areas it controls that provides healthcare, police training, sanitation and even guided tours of the region's famous mountain gorillas for a few rare tourists.
"Before, we didn't have medical services," said Jean Sebagabo, a 37-year-old cattle farmer in Runyoni, which has been under rebel control for months. "Now the rebels are providing free treatment to my son."
Such activities are aimed at embarrassing Kabila, whose support in the east of the country has slipped in recent years, largely over his failure to defeat armed groups roaming the forests despite help for him from United Nations peacekeepers.
"Joseph Kabila has shown he can't run the country," said Bishop Jean Marie Runiga, civilian president of M23. "The population is living in appalling poverty, the army doesn't work, the police doesn't work, so why go on supporting this president?"
He added that M23 had renamed its armed wing the Congolese Revolutionary Army - or ARC in its French acronym - as part of efforts to brush up its image.
"We decided to give the army that name to show we're not a rebellion but a revolution, which will bring change," he said. "M23 is ... a movement for everyone."
In a country which has slumped to the bottom of the U.N.'s human development index after nearly two decades of conflict that has killed millions and left roving bands of gunmen in its wake, the approach is winning some supporters.
"Its a problem of governance, there no food there's no money," Rashidi Benshulungu, an intelligence officer in Kabila's army who defected to the rebels, told Reuters in Goma.
Hundreds of other Congolese troops have defected since clashes escalated this month, helping swell M23's fighting force to as many as 4,000, from a few hundred in April.
But the effort to win over broad support from Congolese generally will also present hurdles, due to simmering hatred of Rwanda, and deep-seated ethnic tensions.
A previous Rwanda-backed rebellion in 2008 claimed hundreds of lives in North Kivu province as insurgents killed, raped and recruited children to their ranks. Many leaders of the former rebellion, including international war crimes fugitive General Bosco Ntaganda, have taken up top roles in M23.
The group was formed when soldiers rose up eight months ago, contending Kabila's government violated a 2009 peace deal that was meant to integrate them into the army. Its name refers to the March 23, date of the 2009 deal.
M23 "say they want to change the situation, but it's lies, they're just trying to trick us", said Justin Bayene, an apprentice in Sake, a town near Goma which fell on Wednesday to M23 with little resistance.
M23's original decision to base its grievances on the 2009 peace agreement may also harm its chances of winning over much of the population, according to Jean Paul Lumbulumbu, a lawyer and rights activist in Goma. Referring to a widespread view that that accord had been too generous to the rebels, he said:
"The angle they started with now was a mistake." (Editing by Richard Valdmanis and Alastair Macdonald)