“The airport is under the control of the M23,” a United Nations official said on condition of anonymity, referring to the rebel group of former soldiers who mutinied in April, setting off the latest cycle of violence in the chronically unstable area.
A column of rebel fighters was seen heading from the airport toward Goma proper, several kilometres away, according to an AFP photographer on the scene.
Loud explosions shook the area and there were reports of looting.
The city of 300,000 is the regional capital and currently is also sheltering tens of thousands of refugees who have fled the clashes.
The international community has raised alarm about the fighting, which has sparked fears of a wider regional conflict in the region.
The UN accuses neighbouring Rwanda and Uganda of backing the rebels, charges both countries deny.
Washington has warned the fighting was “an extremely dangerous and worrying situation” and the EU, Britain and France have also raised alarm.
The latest round of fighting erupted last week after the US and the UN slapped sanctions on the leader of the M23.
The rebels have said they plan to fight the DR Congo government “until it falls”, and the United Nations warned they have a real possibility of capturing Goma.
The UN has some 1,500 “quick reaction” peacekeepers in Goma, part of some 6,700 troops in the Nord Kivu province, backing government forces against the rebels.
Aid agencies have evacuated staff from the city and the UN had planned to remove non-essential personnel on Tuesday.
On Monday Kinshasa rejected the rebels ultimatum for direct talks within 24 hours, calling it “irrational rantings.”
“We prefer to negotiate with Rwanda, the real aggressor,” government spokesman Lambert Mende told AFP.