M23 rebels backed by Rwanda claim to have taken control of Goma – the largest city in eastern Democratic Republic of Congo.
The government says the Rwandan army is also in Goma.
It urged residents to stay at home, amid reports of mass panic and hundreds of thousands fleeing the city.
Rwandan and Congolese troops have also been firing at each other across their border.
And the capture of Goma fuels fears of a full-blown war between the two countries, in a mineral-rich region where fighting has already displaced millions.
But Kenya says their presidents have agreed to meet on Wednesday.