M23 rebels march on strategic eastern town of Bukavu after seizing provincial capital of Goma earlier this week.
"President Museveni and President Kagame made it clear that even if there were legitimate grievances by the mutinying group known as M23, they cannot accept the expansion of this war," the statement added.
They also cannot "entertain the idea of overthrowing the legitimate government of the DRC, or undermining its authority."
Earlier on Wednesday, thousands of government soldiers and police in the DR Congo surrendered to rebels at a stadium in Goma, the main city in the eastern North Kivu province.
Troops hand over weapons to the M23 rebels
A rebel group seeking to overthrow the Congolese government has focused its aim on seizing the strategic eastern town of Bukavu, which would mark the biggest gain in rebel territory in nearly a decade if it were to fall.
The fighters, believed to be backed by neighbouring Rwanda, already have seized the provincial capital of Goma this week and later took the nearby town of Sake on Wednesday.
The violence has forced more than 100.000 people to flee, more than half of whom are children, according to the UN children's agency.
While they have vowed to overthrow President Joseph Kabila's government, they remain some 1.600km from the capital of Kinshasa in a country of dense jungle with few paved roads.
Meanwhile, hundreds of Congolese soldiers who had retreated from Goma days earlier were holed up in Minova, a lakeside city on the road to Bukavu.
"We are waiting for orders, but they haven't come yet. We're hungry and have spent five days sleeping in the bush under the rain," said a Congolese army major who spoke on condition of anonymity because of the sensitivity of the matter.
After capturing Goma on Tuesday, the rebels advanced onto the town of Sake on Wednesday. They now say they are preparing to march into Bukavu, the other major city on the border with Rwanda.
The M23 then plans to head to Kisangani, and onto the capital Kinshasa.
The drive by the rebels was causing some fear in other parts of the country, Al Jazeera's Haru Mutasa reported from Kinshasa.
"People are very very nervous about what will happen … and the fact that the army doesn't seem to be in control of the east of the country," she said.
Al Jazeera's Nazanine Moshiri reported from a camp near Goma, where 19.000 families had arrived in recent days.
"They don't have enough food, they don't have enough shelter for them," she said. Fighting continued not far from the camp, she said, in the town of Sake.
The rebels were told to pull out a day after they captured the city, in a joint statement released on Wednesday in the Ugandan capital Kampala after DR Congo President Joseph Kabila met his Rwandan and Ugandan counterparts, Paul Kagame and Yoweri Museveni, to resolve the crisis in Goma.
"M23 must immediately stop [its] offensive and pull out of Goma," the three presidents said in the statement. "A plan to this end is being communicated to them," the statement said.
The United Nations accuses Rwanda of backing M23 fighters who now control the key eastern town of Goma and take their name after a peace agreement they signed with the Congolese government on March 23, 2009.
Kigali denies the charges and Uganda has also dismissed accusations it has aided the rebels. Rwanda for its part accuses Kinshasa of renewing co-operation with Rwandan rebels based in eastern DR Congo.
'Causes of disturbances'
"The government of the DRC, on its part, has made a commitment to look expeditiously into the causes of disturbances and address them as best they can," the statement added, read out by Ugandan foreign minister Sam Kutesa.
Al Jazeera's Nazanine Moshiri reported on "extraordinary scenes", as the security officers came to hand in their arms.
"[The surrendered officers] didn't have a choice," she said.
The soldiers were told they had a choice either to have peace in the city, or to leave the city, she said.
M23 seized Goma on Tuesday, in a development that raised fears of a new, regional conflict.
The capture of the city came after days of fighting with government troops.
The peacekeepers were not helping the government forces during Tuesday's battle because they do not have a mandate to engage the rebels, said Congolese military spokesperson Olivier Hamuli.
Our correspondent said people appeared to be frustrated with what they see as the UN's lack of action in protecting them from rebel groups.
According to a UN official, protesters were throwing stones and burning tires at the premises MONUSCO, as the peacekeeping force is known, in at least three cities on Wednesday.
Peacekeepers were on alert and UN staff were re-grouping at secure locations as a precautionary measure, the spokesman said.