(Adds details about Lavrov conversation with German minister)
MOSCOW, May 3 (Reuters) - Russian Foreign Minister Sergei Lavrov has told his U.S. counterpart John Kerry that the U.S. should use its influence to make Ukraine's government immediately stop military operations in south-east Ukraine, the Russian foreign ministry said on Saturday.
Lavrov also said that it was important that the mediating role of the Organization for Security and Cooperation in Europe (OSCE) was increased to secure Kiev's fulfilment of the Geneva declaration on de-escalating tensions in Ukraine.
"Chances of this still exist," the ministry said in a statement, as long as all Ukrainian regions are represented in a national dialogue on constitutional reform, and "terrorists" from the Right Sector - a Ukrainian nationalist group in western Ukraine - group are curbed.
Lavrov, in a phone conversation with German Foreign Minister Frank-Walter Steinmeier, also said he was concerned about reports that Ukraine's army was preparing to storm cities in south-east Ukraine including Slaviansk, according to a statement from the foreign ministry.
The town of Slaviansk in eastern Ukraine has been turned into heavily fortified redoubt by pro-Russian separatists.
On Saturday Ukraine said it was pressing on with an offensive in the area for a second day, and had recaptured a television tower and a security services building from rebels in Kramatorsk, a town near the rebel stronghold of Slaviansk.
Steinmeier agreed that violence should halt, the statement said.
(Reporting by Jason Bush and Megan Davies; Editing by Stephen Powell)