Rwanda said Monday it would step up border monitoring and urged its citizens to avoid "unnecessary" travel to the eastern DRC.
"To build trust we must demonstrate we are not parachuting in to deal with Ebola and leaving once it's finished", he told yesterday's meeting in Geneva.
More than 1600 people have died in this year-long outbreak.
The haemorrhagic virus outbreak, the second deadliest on record, has largely been contained in remote parts of DR Congo. But efforts to roll back Ebola have been hampered by insecurity in a region plagued by militia groups, who have attacked treatment centres.
At the event yesterday, the International Development Secretary expressed his deepest condolences following the death of two Congolese Ebola health workers over the weekend. Goma's health ministry has been preparing for an outbreak.
The patient who brought Ebola to Goma was a priest who became infected during a visit to the town of Butembo, 200 kilometers north of Goma, where he interacted with Ebola patients, Congo's health ministry said in a statement.
There, he preached at seven churches and regularly touched worshippers, "including the sick", the health ministry said Sunday. The patient did not exhibit any symptoms of the blood-borne virus at any of the health check-points along the journey from Butembo to Goma.
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Health officials also report that through communication with the transportation company that operates the bus, all of the other 18 passengers and the driver of the bus have been successfully contacted and will receive the experimental Ebola virus vaccine.
"During the checks, he did not seem to show signs of the disease". The ministry says that risk of the disease spreading is low.
World Health Organisation (WHO) teams started vaccinations against Ebola in Goma on Monday, focusing particularly on people who were on a bus with the pastor from Butembo to Goma.
World Health Organization and partners have also said the response has been hampered by a lack of resources, repeatedly citing a $50 million gap in its Ebola containment plan. "The identification of the case in Goma could potentially be a game-changer in this epidemic", Tedros warned.
The committee has been convened three times in the past to decide whether or not the epidemic warrants being declared a global emergency; it has declined every time to do so.
In cities, density of population, high mobility and anonymity make it far harder to isolate patients and trace contacts compared to the countryside. The city of more than 2 million is on the border with Rwanda. It has a port that links to Bukavu and South Kivu and an airport with flights to Kinshasa, the Ugandan capital Entebbe and Addis Ababa, the capital of Ethiopia.
While the epidemic has become the second deadliest in history, with almost 1,700 killed in Congo, its spread to neighboring African countries has been mostly contained.