"The main component of the plan is starting a direct dialogue," Steinmeier told journalists after talks with Georgian Foreign Minister Yekaterina Tkeshelashvili in Tbilisi.
Germany has proposed a three-stage plan for resolving the Georgia-Abkhazia conflict. The plan stipulates a commitment to non-violence by all the parties involved in the conflict, the gradual return of Georgian refugees to the region, and the eventual determination of the political status of Abkhazia.
"Based on this plan we should find a way out. You will have strong support from the European Union," Steinmeier said, adding that he hoped the UN would also express its approval of the plan.
Steinmeier is to fly to Abkhazia on Friday. He will then fly later in the day to Moscow for further talks.
Russian Foreign Minister Sergei Lavrov said earlier in the day that Western nations were blocking Moscow's plans for a non-aggression pact between Georgia and its rebel region of Abkhazia by insisting on the return of Georgian refugees.
"Signing an agreement on Georgian refugees' return to Abkhazia is impossible at the moment, as the situation first needs to be improved and trust restored. Only then can discussions be held on the matter," he said.
Around 300,000 Georgians fled fighting in Abkhazia during a 1992-93 separatist war as the republic looked to break away from Tbilisi. Some 10,000-30,000 people were killed in the conflict.
Russia had earlier presented a draft resolution to the United Nations Security Council calling for a deal on the non-use of force between Georgia and Abkhazia, amid rising tensions and growing fears of a new conflict in the area.
Moscow had earlier also demanded that Georgia first withdraw troops from the upper part of the Kodori Gorge, occupied in 2006 in violation of a 1994 ceasefire agreement.
Georgian President Mikheil Saakashvili has also made the return of the refuges a condition for restarting peace talks with Abkhazia. He also demanded that Russia withdraw its peacekeepers from the conflict zone and end financial support for the region.
Relations between Russia and Georgia have sunk to a new low recently, with outbreaks of violence in Abkhazia and South Ossetia, another Georgian breakaway republic.
