(CNN) -- Congolese rebels took control of the eastern city of Goma and part of the border with Rwanda on Tuesday after days of heavy clashes, a Congolese reporter there said.
The rebels took control of the government radio station in Goma and were seen walking through town, entering government and police buildings, said the reporter, who could not be named for security reasons.
The rebels are part of the M23 rebel group, which has been engaged in heavy fighting with Congolese army forces in the region since last Thursday.
Though 1,500 United Nations peacekeeping troops are in Goma and have control of the airport there, a U.N. spokesman said the situation is at a "critical stage."
"Reports indicate that the M23 has wounded civilians, is continuing abductions of children and women, is destroying property and is intimidating journalists and those who have attempted to resist their control," said Eduardo del Buey, the deputy spokesman for the U.N. secretary-general.
A total of 6,000 troops from the U.N. mission in Congo, MONUSCO, are in the wider region of North and South Kivu, patrolling areas of particular insecurity, del Buey said.
The United Nations, the African Union and countries in the region are demanding that M23 immediately stop its attacks, Buey said.
France and Britain expressed their concerns Tuesday. The British Foreign Office said its minister for Africa, Mark Simmonds, was traveling to Rwanda, Congo, and Uganda to support efforts to end the crisis.
"I am deeply concerned by the current crisis and I urge the M23 to stop their offensive and for all external support to the M23 to cease," Simmonds said in a statement ahead of the visit.
The conflict spread over the border Tuesday when several shells hit Rwanda, killing two people and wounding several others, Rwandan Foreign Minister Louise Mushikiwabo told CNN.
An M23 rebel spokesman, calling his group the Revolutionary Army of Congo, went on the radio Tuesday afternoon to address the people of Goma. Lt. Col. Vianey Kazarama said the group was there to protect the population and that people should return to work Wednesday.
Any remaining pockets of the army should join the rebels or the M23 will fight against them, Kazarama said. He called on members of the police and army still in Goma to meet with the rebel leadership Wednesday morning to hand over their weapons and uniforms and join the rebels' cause.
The group has already started recruiting new members at the police headquarters in Goma, according to the Congolese reporter on the scene.
Several high-ranking government officials have fled Goma for nearby Bukavu, in South Kivu, U.N. officials and a senior NGO official said earlier Tuesday.
The local Goma government could not be reached for comment. Nor could MONUSCO, which is mandated to protect civilians in Goma.
The eastern part of Congo, which includes Goma, has been embroiled in violence since 1994, when Hutu forces crossed the border from Rwanda fearing reprisals following the genocide.
Soldiers from the M23 group were part of the national army as part of peace negotiations brokered in 2009. They broke away from the Congolese army in April, however, complaining of a lack of pay and poor conditions.
One of its commanders, Bosco Ntaganda, is wanted by the International Criminal Court for war crimes, including recruiting child soldiers.
Security analysts say the rebellion in eastern Congo has dangerous regional implications, and the international community has expressed alarm at the M23 advances.
British Foreign Secretary William Hague condemned M23's advance into Goma and said anyone responsible for rights abuses would be held to account.
"The M23 must withdraw their forces immediately and allow legitimate government control to be restored. The cessation of hostilities and the protection of civilians is paramount," he said in a statement.
The International Crisis Group, an independent anti-conflict non-profit group, warned that the fall of Goma could lead to serious human rights abuses against civilians. The settling of scores or even extrajudicial killing of members of the authorities and civil society activists who have opposed M23 could fuel further violence, it said.
The unrest could also spread to neighboring communities and "relaunch open warfare between the DRC and Rwanda," the group said on its website.
The United Nations and some donor countries have accused neighboring Rwanda of backing the M23 rebel group by providing it with arms, support and even soldiers.
Rwandan President Paul Kagame has repeatedly denied the allegation, and Mushikiwabo said Tuesday Rwanda has moved "way past" the accusations.
Rwanda will not engage in any talks with M23, Mushikiwabo said. "Our interlocutor is the government of the DRC," she said.
Mushikiwabo said Rwanda would close the border crossing if asked to by the Congolese government, but that such a move could have humanitarian consequences.
Tens of thousands of Congolese, already displaced by previous rounds of fighting in the volatile region, have fled camps around the edges of Goma, according to UNICEF and the medical charity Doctors Without Borders.
CNN's Michael Martinez contributed to this report.