"The Ministry of Health confirms that Rwanda's border with the Democratic Republic of Congo is open, following traffic slow-down this morning as measures were put in place to reinforce screening procedures and public safety at entry points", the statement said.
The announcement to close the border came just hours after a third case of Ebola was recorded in Goma, widening the scope of the epidemic on its first anniversary.
The new cases have stoked fears the virus could take root in the city of more than 1 million people.
This third confirmed case is the first transmission of Ebola inside Goma during this outbreak, as the previous two patients are thought to have contracted the disease elsewhere.
The first confirmed case in Goma was a 46-year-old preacher who managed to pass through three health checkpoints on the way from Butembo.
"The Congolese authorities deplore this decision, which runs counter to the advice of the WHO (World Health Organisation)", on fighting the virus, the Congolese presidency statement said.
It has also said the risk of regional spread was "very high".
The deadly Ebola outbreak in Congo now enters its second year.
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Rwanda has restricted movement across its border with DR Congo, where an Ebola outbreak has killed more than 1,800 people in the past year.
Rwanda's state minister for foreign affairs Olivier Nduhungirehe confirmed the border closure to The Associated Press, a day after World Health Organization officials had praised African nations for keeping their borders open. The man was diagnosed a few days after arriving in Goma from a northeastern rural community in Congo's Ituri province.
The Associated Press reported that the latest victim, a miner in his 40s, had shown symptoms of the disease after returning to Goma and died July 31 at an Ebola treatment center. It is not immediately clear whether the person is a family member of the man who died on Wednesday. Though he said there is an "agreement" that there should be more than one licensed Ebola vaccine available for long-term use, US agencies have been "deferring to local health authorities for which vaccines are available for use".
Rwanda's ministry of health denied the border was ever closed, and by Thursday afternoon people were crossing between the cities again.
Until the Goma cases, no major cities had been affected by the epidemic.
- There have been at least 198 attacks on Ebola health facilities and health workers in the Congo since January, as health workers face a militia violence and local mistrust over the response.
There is no licensed treatment for Ebola and many people in the region don't believe that Ebola is real, health workers have said.
"The UK has led the way in tackling this killer disease and we can be proud of our support to create a life-saving Ebola vaccine which has inoculated 180,000 people so far".