"I had a difficult, long and very serious talk but it wasn't enough to say that a solution is in sight," Steinmeier told reporters after the meeting with Lavrov late on Monday.
"I can't run up a flag to say that we are on the way to finding a solution and that Ukraine and Russia are about to start talking."
Germany has been attempting to bring Russia and Ukraine to the negotiating table to defuse the crisis which was sparked when thousands of Russian troops landed in the Crimea.
The German foreign ministry has stressed that dialogue must be kept open with Russia and has reacted coolly to suggestions by the US that the country should be barred from the G8 and sanctions imposed.
Steinmeier is also meeting UN General Secretary Ban Ki-moon in Geneva on Tuesday.