The M23 rebels announced the city's capture in a statement minutes before a 48-hour deadline given to the Congolese army to surrender expired.
In a statement, the rebels urged residents of Goma to remain calm and for members of the Congolese military to assemble at the central stadium.
The rebels have made lightning advances in January in the Democratic Republic of Congo's mineral-rich, conflict-riven eastern borderlands and launched an assault on Goma earlier this week.
Residents have been fleeing after rebels invaded the outskirts of Goma. (AP PHOTO)
By Sunday evening, M23 fighters had pushed past Munigi, an outlying neighbourhood around nine kilometres from the city centre, three sources told Reuters.
The rapidly deepening conflict is aggravating one of the world's worst humanitarian crises and has raised fears the fighting could spill over into a broader regional war.
Congolese government spokesman Patrick Muyaya posted a video on social media platform X calling for the protection of civilians and saying the country is "in a war situation where the news is changing".
The United Nations Security Council met earlier on Sunday to discuss the crisis, in which three UN peacekeepers - a Uruguayan and two South Africans - have been killed in the last two days.
Western nations have condemned what they say is Rwanda's support of the rebel campaign. (AP PHOTO)
The United States, France and Britain on Sunday condemned what they said was Rwanda's backing of the rebel advance. Kigali has long denied supporting M23.
Rwanda's UN ambassador Ernest Rwamucyo said his country regretted the deteriorating situation in eastern Congo, but blamed Kinshasa.
"The current crisis could have been averted had (Congo's) government demonstrated a genuine commitment to peace," he added.
The eastern borderlands of Congo, a country roughly the size of western Europe, remain a tinder-box of rebel zones and militia fiefdoms in the wake of two successive regional wars stemming from Rwanda's 1994 genocide.
With AP
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