The group of eight men, all Europeans, were part of a 12-member OSCE military verification team being held in east Ukraine. The other four are Ukrainian military officers who were not brought before the press.
Speaking through one of their number, a German officer, the Europeans asserted their diplomatic status to the scores of local and foreign journalists assembled in the town of Slavyansk.
With armed rebels watching over them as they spoke, the group said they were in good health.
"We are OSCE officers with diplomatic status," German officer Axel Schneider said.
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"I cannot go home of my free will."
Schneider added that he did not know the whereabouts of the four Ukrainian officers grabbed with them.
The Organisation for Security and Cooperation in Europe said it has sent a negotiating team to Slavyansk to try to arrange the entire team's release.
Earlier, the local rebel leader in the town, Vyacheslav Ponomaryov, told AFP and a small group of other reporters the OSCE observers were considered "prisoners of war".
Ponomaryov, who was wearing a pistol in a holster and was escorted by two armed bodyguards, claimed in the same interview that the observers "are not our hostages -- they are our guests".
The rebel leader said all "are doing well".
He added that the group's driver, who had been seized with them on Friday, had been released.
He repeated in the interview that the men would only be freed in exchange for Kiev's authorities releasing arrested pro-Moscow militants.