The self-styled mayor of rebel-held Slavyansk, which has become the epicentre of the crisis, led eight European members of an OSCE military inspection mission before scores of local and foreign journalists in the town hall.
With four armed rebels watching over him, a spokesman for the group, German officer Axel Schneider, said the team was in good health and stressed they were "OSCE officers with diplomatic status".
"I cannot go home of my own free will," he told reporters, adding that negotiations were under way to free them.
Ukraine's foreign minister said the OSCE's head, Lamberto Zannier, was on his way to Kiev to mediate in the crisis but the organisation's Vienna headquarters later denied this.
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Pro-Russia militias this month occupied a string of towns and cities in eastern Ukraine, sparking a military response from the Ukrainian army, which is laying siege to Slavyansk.
The detention of the men from the Organisation for Security and Cooperation in Europe has sparked global outrage amid the worst East-West crisis since the end of the Cold War.
The international community is on edge, with one Western diplomat raising the possibility of an invasion in the coming days by Russia, which has some 40,000 troops massed on the border.
Speaking in Asia, Obama called for global unity as Europe and the US prepare fresh sanctions against Moscow expected to come into force as early as tomorrow.
Obama said Russia had "not lifted a finger" to implement a deal struck in Geneva on April 17 aimed at easing the crisis.