Mr Steinmeier was speaking after a meeting with his Russian, Ukrainian and French counterparts in Berlin.
Earlier, the head of the OSCE monitoring group said a renewed ceasefire had opened up a window for political progress.
The leaders of Russia, Ukraine, Germany and France are due to meet in Paris in early October to discuss efforts to resolve the Ukrainian conflict.
Almost 8,000 people have been killed since fighting began in April 2014.
Mr Steinmeier said all parties reaffirmed that the ceasefire, which has held for almost two weeks, needed to be consolidated.
The warring sides were now “very close” to a deal that would see the withdrawal of heavy weapons from the frontline, he added.
He also said there was some progress on the legal groundwork towards holding local elections in eastern Ukraine in October.
Ukraine is due to hold its elections on 25 October, while separatists in the rebel-controlled Donetsk and Luhansk regions have said they would hold their own votes on 18 October and 1 November respectively.
Russian Foreign Minister Sergey Lavrov told reporters in Berlin that a deal was “90 per cent ready” but said the “devil is in the detail”.
Leaders of France, Germany, Russia and Ukraine are due to meet again at a summit on 2 October in Paris.
A calmer atmosphere has been reported in separatist-controlled areas of eastern Ukraine.
In an interview with the AP news agency on Saturday, OSCE chief Lamberto Zannier said the ceasefire in eastern Ukraine had opened space “to make progress on a political level”.
Mr Zannier said he had visited Mariupol and Shyrokyne - the scene of recent clashes - and found the situation to be calm.
The area is on the front line between Ukrainian government forces and pro-Russian rebels and has seen some of the fiercest fighting.
Russian President Vladimir Putin also mentioned the ceasefire on Saturday, describing it as the “main achievement” of the peace process to date.
A ceasefire was declared in February but Ukrainian troops and Russia-backed separatists carried on fighting until a renewed truce was pledged on 1 September.
Last week, Ukrainian Defence Minister Stepan Poltorak said fighting had fallen to its lowest level since the conflict started.
Earlier this month a grenade exploded outside Ukraine’s parliament during a nationalist protest against a vote to give greater powers to separatist regions in the east, killing a police officer.