The African Union's health watchdog announced on Thursday that an outbreak of the deadly Marburg virus in Rwanda is now under control, with "almost zero risk" of it spreading beyond the country's borders.

The outbreak, resembling Ebola, was first reported in late September, prompting the launch of a vaccination program utilizing a trial vaccine over the weekend.

"The outbreak in Rwanda is controlled," Jean Kaseya, head of the Africa Centres for Disease Control and Prevention (Africa CDC), said at an online briefing.

The small nation in the Great Lakes region of Africa has recorded up to 58 cases of the disease, with 13 deaths, Rwandan Health Minister Sabin Nsanzimana told the briefing.

He said 12 people have recovered, while more than 2,700 have been tested.

"We estimate the case fatality rate to be about 22 percent, and we want to keep this as low as possible."

With a fatality rate of up to 88 percent, Marburg's highly infectious hemorrhagic fever is often accompanied by bleeding and organ failure.

At Thursday's briefing, Kaseya said Rwanda had recorded no new cases or deaths in an update the day before, adding, "It means we are expecting to see Rwanda out of this outbreak very soon."

He also said there was "almost zero risk" of the virus spreading across the borders of the landlocked country.

"It's 95 percent certain there is zero risk for Rwanda to spread the disease out of Rwanda."

On Monday, the United States urged its citizens to reconsider traveling to Rwanda because of Marburg.

Kigali also announced on Wednesday that in the wake of the outbreak, it was postponing its annual baby gorilla naming ceremony scheduled for October 18.

The event aims to raise awareness of the need for mountain gorilla conservation and promote tourism.