"I hope that by the end of June there will be progress and then we can see if we can reduce the sanctions step by step, or if we stay with the measures we have right now," Steinmeier told reporters in Tallinn.
"It is not our aim to maintain the sanctions but to resolve the conflict."
EU sanctions imposed on Russia's banking, defence and energy sectors over its actions in neighbouring Ukraine expire in July.
But yesterday, Steinmeier said the European Union was facing difficult talks on extending the sanctions because of the increased resistance of some member states.
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He did not name names, but Italy and Hungary have been among the most sceptical while Poland and the Baltic states -- fearful of Russia's actions in their backyard -- have repeatedly pressed hard for sanctions to maintain pressure on Moscow.
German Chancellor Angela Merkel, speaking in Japan, also said yesterday that the Group of Seven has no plan to withdraw its sanctions on Russia.
Germany and France helped broker peace accords for Ukraine signed in the Belarusian capital Minsk in 2015.
They call for a ceasefire along with a range of political, economic and social measures to end the conflict in eastern Ukraine that has claimed more than 9,300 lives since April 2014.