A U.N. official said fighters from the M23 rebel group were seen roaming about Goma Tuesday afternoon and had seized the border crossing with neighboring Rwanda, along with several other parts of the city, CNN reported.
Intense fighting was reported at Goma's airport, but witnesses said it wasn't clear whether rebels had captured that strategic point.
Local radio stations had gone quiet as of Tuesday morning.
Heavy shelling and small arms fire were heard overnight in Goma after a 24-hour deadline issued by the M23 rebels to negotiate passed, CNN said. Independent radio stations reported the Congolese government refused to meet the M23's deadline.
Several high-ranking government officials fled Goma for Bukavu in South Kivu, U.N. officials said.
Local government officials and the U.N. peacekeeping force charged with protecting Goma citizens could not be reached for comment, CNN said.
The eastern part of Congo has been embroiled in violence since 1994, when Hutu forces crossed the border from the nation of Rwanda out of fear of reprisals following the genocide of Tutsi.
M23 soldiers were considered part of the Congolese national army under a 2009 peace negotiation. However, they broke from the government army in April, complaining of poor conditions and lack of pay.
One M23 commander, Bosco Ntaganda, is wanted by the International Criminal Court for war crimes, including child-soldier recruitment.