BERLIN (Reuters) - German Foreign Minister Frank-Walter Steinmeier urged Ukraine's government on Saturday to exercise caution in using military force against pro-Russian separatists in the eastern part of the country.

"The result of military operations in eastern Ukraine must not be to give more impetus to the separatists," Steinmeier told Tagesspiegel am Sonntag newspaper in extracts released on Saturday, the same day a new president was inaugurated in Kiev.

In such a tense situation, he added, it would be "smart to be cautious in the deployment of military force and have a sense of proportion".

Steinmeier also said Russia's behavior in the conflict had "noticeably changed", a comment that appeared to strike a new tone in emphasizing the importance of both Kiev and Moscow taking responsibility for a de-escalation.

Germany has repeatedly called on the Kremlin to help stabilize Ukraine following Russia's annexation of Crimea in March and a standoff in eastern Ukraine between government forces and pro-Russian separatists.

During ceremonies in France marking the 70th anniversary of the World War Two D-Day landings on Friday, Chancellor Angela Merkel told Russian President Vladimir Putin that Russia had a "great responsibility" to help bring peace to Ukraine.

Steinmeier also said that Russia must do what it could to help stabilize the situation and that it was "important for Moscow to publicly support the territorial integrity of Ukraine and reject all efforts aimed at a division."

He said both sides had to secure their common borders to prevent an influx of weapons and fighters from Russia.

Ukraine's Petro Poroshenko sent a defiant message to Russia on Saturday in his inaugural speech as president, saying his country would never give up Crimea and would not compromise on its course towards closer ties with Europe.

Since his election, government forces have stepped up their operations against separatist rebels in eastern Ukraine who want to split with Kiev and become part of Russia. But rebels have fought back and parts of eastern Ukraine have become a war zone.

(Reporting by Madeline Chambers; Editing by Tom Heneghan)