"Yesterday, we arrested some NATO spies… they will be exchanged for our own prisoners. I don't see any other way they will be freed," Denis Pushilin, the head of the insurgents' self-declared Donetsk Republic, told reporters.
Pushilin was speaking in front of the SBU security services building in rebel-held Slavyansk, where the OSCE team was being held.
The town's self-styled mayor, Vyacheslav Ponomaryov, also told Russian TV news crews that the OSCE members were being considered "intelligence officers of NATO country members".
"Military personnel from Denmark, Germany, Poland, the Czech Republic, Bulgaria I think and – from somewhere else, I can't immediately recall – have been detained," he said in broadcasts seen in Moscow.
"We believe an OSCE mission does not imply the participation of military personnel entering our territory unimpeded and studying our facilities."
Slavyansk has become the epicentre of tensions between pro-Russian protesters and Ukrainian authorities in the eastern part of the country where pro-Kremlin rebels have seized a string of towns.
Late Friday, German Defence Minister Ursula von der Leyen confirmed that pro-Russian separatists had arrested 13 mission members, including the observers, their interpreter and driver. Four of the team are Germans, including three members of the German military.
Swedish Foreign Minister Carl Bildt said on his Twitter feed that one of the OSCE members was a Swede.
On Saturday, authorities in Berlin said that Foreign Minister Frank-Walter Steinmeier had called his Russian counterpart Sergei Lavrov to demand Moscow use its influence to secure the group's "immediate release."
"We are using all the means at our disposal to… ensure that they can continue their mission," the foreign ministry said in a statement.
The ministry added it had also been in contact with "high-ranking Russian diplomats" in Berlin over the situation.