M23 rebels took control of the city Tuesday and have refused to leave unless DRC President Joseph Kabila agrees to peace talks, Sky News reported.
"There must first be a dialogue with President Kabila," M23 leader Jean-Marie Runiga Lugerero said.
British Prime Minister David Cameron spoke with the presidents of Rwanda and the DRC by telephone Thursday.
A Downing Street spokesman said: "(Cameron) used the calls to welcome the joint communique signed by [Rwandan] Presidents [Paul] Kagame, Kabila and [Ugandan politician Yoweri] Museveni condemning the M23 rebel group and calling on them to pull out of Goma."
"He made clear that the international community could not ignore evidence of Rwandan involvement with the M23, and that President Kagame needed to show that the government of Rwanda had no links to the M23,"
The United Kingdom's minister for Africa, Mark Simmonds, arrived in Kigali, Rwanda, Thursday, CNN reported.
Simmonds said, "There can be no attempt to unseat the legitimate government of the Democratic Republic of Congo" and called on the Congolese government to "address the underlying causes of the conflict."
"I call on the M23 to stop its advance and to withdraw from Goma immediately," Simmonds said.