On Sunday negotiators from the pan-European security body walked out of a rebel-occupied town hall in east Ukraine with just one of the eight OSCE inspectors being held as "prisoners of war" by pro-Kremlin separatists.
Later that day, Burkhalter said the detention of the unarmed military inspectors and their hosts from the Ukrainian defence ministry was "unacceptable and that the safety of all international observers in the country must be guaranteed and ensured".
While welcoming the release of the Swedish OSCE observer as "a positive step", the OSCE said it was continuing to "work at all levels. . . to assist for the release of all the detained persons" including through "high-level political contacts".
Burkhalter said the kidnapping went against the spirit of a deal reached in Geneva on April 17 between Russia, the United States and the European Union to "de-escalate" tensions in Ukraine.
A rebel spokeswoman said the Swedish observer was freed first because he suffers from diabetes.
Still being held early Monday were the other seven European inspectors -- from Germany, Poland, the Czech Republic and Denmark -- and four Ukrainian army officers who were seized with them on Friday, the spokeswoman told AFP.
Hours earlier, the rebels had put the eight OSCE inspectors in front of the cameras at media conference.
Speaking through a German member of their group, the Europeans asserted their diplomatic status to the scores of local and foreign journalists.
With four armed rebels watching over them as they spoke, the OSCE observers said they were in good health.
They said they had been captured by the insurgents on Friday around four kilometres (two miles) outside Slavyansk, as they were about to return to the regional hub city of Donetsk.
"We are OSCE officers with diplomatic status," German officer Axel Schneider said.
"I cannot go home of my own free will."
Schneider added that he did not know the whereabouts of the four Ukrainian officers who were also captured.
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