Nairobi, Kenya (CNN) -- A Congolese rebel group advanced within four kilometers (2.4 miles) of Goma in the violence-riddled eastern region of the Democratic Republic of Congo on Sunday evening, according to eyewitnesses, threatening to take the strategic capital of the region.
Heavy fighting has been reported in recent days as rebel groups battled the Congolese army and U.N. soldiers.
A relative calm on Sunday morning in Goma was broken by fighting close to the town and airport.
"Some government officials and diplomats have fled to Bukavu (in eastern Congo) and across the border to Rwanda," said a journalist in Goma who did not want to be named for his own security.
U.N. Forces in the region of North Kivu said that they deployed attack helicopters and ground troops to respond to the M23 advances on Goma.
The eastern part of Congo has been embroiled in violence since 1994, when Hutu forces crossed the border fearing reprisals following the genocide in neighboring Rwanda.
In 1998 the vast nation -- previously known as Zaire -- became a battleground for eight African countries. More than 5 million people died in the war and its aftermath, making it the deadliest conflict since World War II.
Despite the signing of peace accords in 2003, fighting continues in the eastern part of Congo between various rebel groups and the Congolese army, which is back by U.N. peacekeepers.
Early on Saturday, rebel soldiers launched attacks on several key towns north of Goma using heavy weapons, said the U.N. Congo mission in a press release.
The U.N. Security Council held an emergency session on Saturday, condemning the latest attacks by the M23 rebel group.
"The members of the Security Council strongly condemn the resumption of attacks by the M23 and demand their immediate cessation," said Ambassador Hardeep Singh Puri of India, which holds the Council's rotating presidency.
Soldiers from the M23 group had been part of the national army as part of peace negotiations brokered in 2009. They broke away from the Congolese army in April of this year, complaining about a lack of pay and poor conditions. One of their commanders, Bosco Ntaganda, is wanted by the International Criminal Court for war crimes, including recruiting child soldiers.
The U.N. and some donor countries have accused neighboring Rwanda of backing the M23 rebel group by providing it arms, support and even soldiers.
It is a allegation that Paul Kagame, Rwanda's president, has repeatedly denied. But security analysts say the rebellion in eastern Congo has dangerous regional implications, and the international community has expressed alarm at the latest M23 advancement.
"I call on the M23 to immediately stop the military offensive against the city of Goma. Any support to the M23 in violation of the sanctions ... and the arms embargo must stop," said Catherine Ashton, the European Union foreign affairs chief.
Residents of Goma were close to panic on Sunday, but no one had fled across the border to Rwanda yet.
"But who knows what will happen overnight," said one resident.