All the men deny charges of conspiring to kill Tutsis
Magistrates in London have upheld a request to extradite four men to Rwanda to face mass murder charges.
They are wanted in connection with the genocide in 1994 in which 800,000 people were killed in 100 days.
They are Dr Vincent Bajinya, of London, Charles Munyaneza, from Bedford, Celestin Ugirashebuja from Essex, and Emmanuel Nteziryayo, of Manchester.
All four deny involvement and the decision will now be referred to the Home Secretary Jacqui Smith.
The four men, who were local government officials at the time of the genocide, face charges including genocide and crimes against humanity.
Violence erupted in the African country in 1994 after the Hutu President Juvenal Habyarimana's plane was shot down and ethnic Tutsi rebels were blamed.
As soon as the president's death was announced, killing squads began attacking Tutsis and moderate Hutus across the country.
Thirty people have been convicted of involvement in the killings at the International Criminal Tribunal for Rwanda (ICTR), based in neighbouring Tanzania.
Until last year a number of European nations were reluctant to extradite Rwandan genocide suspects because they would have faced the death penalty if they had been convicted.
But the Rwandan government has now scrapped the death penalty, opening up the way for extraditions.
On Thursday, France extradited another Rwandan genocide suspect, Dominique Ntawukuriryayo, to the ICTR.
Human rights campaign grup Amnesty International said it would be "outrageous" if the men were extradited.
"The criminal justice system in Rwanda falls very short of internationally recognised standards and so there’s a real danger that these men may not receive a fair trial," it said.
It said the men could be charged and given a fair trial in the UK, or sent to a third country where they would be guaranteed a fair trial.