Tharcisse Karugarama, Rwanda's justice minister, told The Associated Press his country had formally requested that the British government hand over the suspects, who face charges of planning genocide as well as crimes against humanity.
"We request that Britain does not become a safe haven for mass killers," he said by telephone from the capital Kigali. "These men are basking under the protection of Britain."
The four are believed to have entered Britain as asylum seekers in 1998 after changing their names, the minister added.
"We have been looking for them since 1994 and had suspicions they may be in Britain but only recently did we establish that fact," the minister added.
A formal request for extradition was made four months ago and British investigators traveled to Rwanda to assess the evidence, he added. "We are now waiting to hear from the authorities," he said.
One suspect, Vincent Bajinya, has been working for a London-based charity as a doctor, according to news reports, helping refugee nurses and midwives gain jobs in Britain.
Rwanda is also seeking Emmanuel Ntezilyayo, Munyaneza Charlesall and Celestin Ugirasebuja, all senior leaders in Hutu militias who carried out genocide related crimes.
All four would face the death penalty if convicted in Rwanda. Karugarama said that may hamper their extradition but added Rwanda was looking to abolish the death penalty.
More than 500,000 minority Tutsis and politically moderate Hutus in Rwanda were killed by Hutu extremists in 1994.