De facto independence
Abkhazia has enjoyed de facto independence from Tbilisi since a separatist conflict in the early 1990s that killed several thousand people and forced hundreds of thousands to flee their homes.
Both Abkhazia and Russia, which backs the separatists, have insisted on a withdrawal of Georgian troops from the Kodori Gorge as a precondition for any further negotiations with Tbilisi.
Bagapsh's rejection of the German peace plan was another setback for Steinmeier, who arrived in the region on Thursday with plans to visit Georgia, Abkhazia and Russia to discuss a way to stop hostilities.
On Thursday, Mikheil Saakashvili, the Georgian president, rejected key elements of the German plan after meeting with Steinmeier, saying that Tbilisi would refuse to rule out the use of force due to what he called Russian provocations.
The German minister, whose country chairs a United Nations group aimed at resolving the tension in Georgia, said the situation in Abkhazia was explosive and that "the spiralling violence must be stopped".
His plan included a three-stage peace proposal drawn up by Berlin, and was presented to the three parties over the last week.
The first step of Berlin's plan would entail an end to violence, confidence-building measures over the next year that could lead to the resumption of direct talks between Georgia and Abkhazia, and the return of about 250,000 Georgian refugees to Abkhazia.
The second stage would involve developing joint reconstruction projects, while the third and most difficult step would determine Abkhazia's future status.
Steinmeier said he sought "a peaceful resolution based on the territorial integrity of Georgia" but said the West was deeply concerned about the recent escalation in the region.
"No one among us has any illusions. I am not here in the region to raise false hopes. But this deadlock must be broken," he said.