"Those who are responsible are being reached through different channels and we're hoping that these people will be released unharmed," Foreign Minister Seyoum Mesfin told journalists. Seyoum did not give any other details about the contacts, the AP says.
He said that the captives are in the Afar region that straddles Ethiopia and neighboring Eritrea but declined to speculate in which country they are being held.
"We urge those who are responsible for this kidnapping to release those people safe, and the earlier, the better," Seyoum said.
The minister emphasized the captives were safe, but advised patience on the matter.
The group - five employees of the British Embassy in Addis Ababa or their relatives - were abducted along with 13 Ethiopian drivers or translators on March 1. Four of the Europeans are believed to be British citizens, including one of Italian origin; the other is French. Five of the Ethiopians are believed to have escaped or been released.