Tension between the Central African neighbours is reaching breaking point over an insurgency in Congo's eastern hills that Kinshasa's government says is orchestrated by Rwanda with designs on the region's mineral riches.
"Rwanda does not intend to respond to provocation coming from the DRC," Rwandan Foreign Minister Louise Mushikiwabo told Reuters. "Issues in (eastern Democratic Republic of Congo) are too serious to be subjected to game playing."
A Rwandan army spokesperson earlier said Congo's military had fired artillery, anti-aircraft and tank rounds into the Rwandan border town of Gisenyi, injuring three people, as fighting raged between Congo's army and advancing M23 rebels.
Guests at a Rwandan hotel near Congo's border ran for cover on Monday afternoon as heavy weapons fire thudded nearby, a Reuters witness said.
Sustained gunfire could also be heard across the border from the direction of the airport in Goma, the capital of Congo's North Kivu province where Congolese troops, some manning tanks, took up positions in the city centre at nightfall.
The M23 halted their advance about 5km from Goma on Sunday.
Congo's government, which has repeatedly accused Rwanda of backing the eight-month M23 rebellion as a means of controlling mineral riches in North Kivu, said on Monday Kigali may have staged the shelling on its own territory.
"We have information that Rwanda has been firing into their own territory to justify a larger intervention," Congo government spokesperson Lambert Mende said, without outright denying reports of Congolese shelling.
Call for calm
A local UN official said Congo's presidential guard unit had fired the heavy weapons into Rwandan territory, though a spokesperson for the United Nations in New York said the reports could not be immediately confirmed.
M23 say they are fighting because Kinshasa broke the terms of a 2009 peace agreement that integrated them into the army as a solution to an earlier rebellion.
UN experts back the government contention that Rwanda, which has intervened in Congo repeatedly over the past 18 years, is behind the M23 revolt. Rwanda denies involvement.
Yoweri Museveni, president of Uganda, also accused by UN experts of arming M23, told UN chief Ban Ki-moon he had spoken to the rebels, in his capacity as head of a regional body, and called for calm, a UN peacekeeping spokesperson said on Monday. Uganda denies supporting the rebels.
In a report to the UN Security Council released on Monday, Ban said he was disturbed by continued external support for M23 and called on "all those responsible to immediately and permanently end this destabilising assistance".
"The sovereignty and territorial integrity of the Democratic Republic of the Congo is inviolable and must be fully respected by all neighbouring countries," Ban said. "Constructive dialogue and engagement between the Democratic Republic of the Congo and its neighbours, especially Rwanda, is vital."
Analysts say Rwanda and Uganda have maintained extensive commercial and military networks in Congo's east since the two countries sent troops into Congo twice in the 1990s and 2000s.
On Monday, the rebels gave the government 24 hours to start talks or face a new onslaught. Kinshasa swiftly rejected the ultimatum, meaning that the worst fighting in the area in four years was only likely to intensify.
Goma's capture would be an embarrassment for President Joseph Kabila, who won reelection late last year in polls that triggered widespread riots in Kinshasa and which international observers said were marred by fraud.
Congo is rich in minerals including diamonds, gold, copper and coltan – used in mobile phones. But little money has been spent on developing a country the size of Western Europe.
The vast nation was wrecked by wars between 1994 and 2003 which killed about five-million people. Many eastern areas are still plagued by violence from a variety of rebel groups, despite UN-backed efforts to defeat them.
M23 is led by mutinying soldiers who rose up eight months ago. They have now fought four days of battles to come close to Goma, home to a million people including hundreds of thousands of refugees who have fled rebel advances elsewhere.
By Monday night, the streets of Goma were largely deserted save for patrols of UN armoured vehicles and Congolese army positions. Tracer fire lit up the sky in the distance.
Officials said, despite fighting on the outskirts and around the airport, Goma remained in government control. The rebels have said they do not plan to capture the city, which lies at on the shore of Lake Kivu.
More than 50 000 people have fled the camps and homes in Goma and on the outskirts of the town and are in desperate need of shelter, water and food, said Tariq Riebl, humanitarian coordinator for British aid agency Oxfam.
"If fighting intensifies further, there are very few places people can go for safety. With almost 2.5 million people now displaced across eastern Congo, this catastrophe requires a concerted humanitarian and diplomatic response," Riebl said.
The UN peacekeeping spokesperson, Kieran Dwyer, said in a statement that non-essential UN staff would start leaving Goma on Tuesday, although troops would stay to protect civilians.
The United Nations has about 6,700 peacekeeping troops in North Kivu, including some 1,400 troops in and around Goma.
Dwyer said the mission had carried out helicopter strikes in support of the Congolese army at the weekend.
"The situation in Goma is extremely tense," Dwyer said. "There is a real threat that the city could fall into the M23's hands and/or be seriously destabilise as a result of the fighting," Dwyer said in a statement from New York.
He said foreign ministers from the Great Lakes regional body chaired by Uganda's Museveni were due to meet on the conflict on Tuesday in Kampala.