German Chancellor Angela Merkel says Russia has a duty to exert influence on pro-Russian separatists in eastern Ukraine.
Merkel made the remark during a phone call with Russian President Vladimir Putin on October 1.
According to a German government spokesman, the two leaders expressed concern that violence was still being used in Ukraine every day.
Merkel said the border between Ukraine and Russia needed to be monitored and the Organisation for Security and Cooperation (OSCE) had a big role to play in that.
She said Germany would continue to support the OSCE mission in Ukraine, adding that it could play an important role in planned local elections in the regions around Donetsk and Luhansk.
Earlier, NATO's new Secretary-General Jens Stoltenberg said the cease-fire in Ukraine presented the chance of a resolution to the Ukraine crisis but Russia still had the power to disrupt the country.
"The ceasefire in Ukraine offers an opportunity but Russia maintains its ability to destabilize Ukraine. Russia remains in breach of international law," Stoltenberg told his first news conference in Brussels as NATO leader.
Stoltenberg also had conciliatory words for Russia, saying he saw no contradiction between aspiring for a constructive relationship with Moscow and being in favor of a strong NATO.
Meanwhile, reports from eastern Ukraine said some 10 people have been killed in shelling in the rebel-held city of Donetsk.
Three people were reportedly killed when a shell exploded in a school playground on October 1.
Several others reportedly died when a shell hit a mini-van in a nearby street.
The blasts occurred as pupils returned to school, after the start of the school year was postponed from September 1 due to fighting between Ukrainian government forces and pro-Russian separatists.
Shelling has repeatedly been reported in Donetsk despite an September 5 cease-fire in the conflict, which has killed more than 3,000 people since April.
The Donetsk airport has been a focus of fighting since the cease-fire.