His remarks in Abu Dhabi come ahead of a new round of talks in mid-June between Iran and the P5+1 powers of Britain, China, France, Russia, the US and Germany.
"Regardless of the general situation which makes cooperation between the US and Russia difficult in some areas at the moment, the negotiations on the Iranian issue have certainly gone further," he said.
"In recent weeks and months they were so encouraging that we maintained a chance of reaching an agreement," he added, after talks with the crown prince of Abu Dhabi, Sheikh Mohammed bin Zayed al-Nahayan.
The next round of talks on resolving Western concerns will take place in Vienna on June 16-20.
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Three days of such meetings two weeks ago made no "tangible progress," with a July 20 deadline for a conclusive agreement looming on the horizon and major issues still outstanding.
"Whether these negotiations can be completed within the agreed time frame cannot be said at the present time," said Steinmeier. "Anyway, there is no sign that anyone wants to go beyond that time frame."
The differences during the last round in Vienna prevented a start being made on an early draft agreement.
Negotiators aim to nail down an exceedingly complex and lasting deal limiting Iran's atomic activities in exchange for a lifting of sanctions.
Failure could have calamitous consequences, potentially sparking conflict -- neither Israel nor the United States rules out military action -- and creating a nuclear arms race in the Middle East.