Eight members of the Organisation for Security and Co-operation in Europe (OSCE) were travelling with five Ukrainian troops when they were seized by pro-Russian separatists in the flashpoint town of Slavyansk.
"We think that these people need to be freed as soon as possible," said Andrei Kelin, Russia's envoy to the OSCE, in comments quoted by ITAR-TASS news agency.
"Russia as a member of the OSCE will undertake all possible steps in this matter."
However, rebels accused the monitors of being "Nato spies" and vowed to continue holding them.
Russian military helicopters in a field near the Russian-Ukrainian border
"They will be exchanged for our own prisoners. I don't see any other way they will be freed," said Denis Pushilin, head of the self-declared Donetsk Republic.
It comes as G7 nations agree new sanctions against Russia as tensions continued in Ukraine.
Senior EU diplomats said they would hold an emergency meeting in Brussels on Monday to discuss the matter.
America says Russian military planes have entered Ukrainan airspace several times, with Washington calling on Moscow to de-escalate the situation.
The claim came from Pentagon spokesman Colonel Steve Warren, who said: "I can confirm that on several occasions in the last 24 hours, Russian aircraft have entered Ukrainian airspace."
A Ukrainian soldier stands guard near Kramatorsk airport in eastern Ukraine
Col Warren urged Moscow to take "immediate steps to de-escalate the situation".
Officials said it was unclear what the intent was, but the aircraft could have been testing radar or engaging in a show of force.
It is the latest sign of a mounting confrontation between Russia and Ukraine.
Russia is increasing military exercises along its border with Ukraine.
This includes moving a range of fixed wing and rotary aircraft, infantry and armoured troops.
Ukrainian Prime Minister Arseniy Yatsenyuk has accused Moscow of wanting to start "a third world war".
Russian foreign minister Sergei Lavrov has warned Kiev it will face justice for a "bloody crime" in eastern Ukraine, where the government has been acting against rebels.
Pro-Russian separatists have seized public buildings in the east of the country and Moscow has been accused of fermenting unrest and separatist sentiment, charges it rejects.
The Kremlin says it has the right to defend Russian speakers if they are under threat, and has deployed extra troops on the border.