President Saakashvili said on August 11 he had signed a ceasefire deal proposed by senior European envoys.
French and Finnish Foreign Ministers Bernard Kouchner and Alexander Stubb, respectively, met Saakashvili overnight and again early on August 11, before traveling to Moscow.
"We have to convince our Russian friends as we have convinced our Georgian friends here," Kouchner said in a live interview with BBC World from Tbilisi after meeting with President Saakashvili.
When asked what would be his and the Finnish foreign minister's message to Moscow, Kouchner responded: "Peace; stop the bleeding."
"It was the duty of the European Union to stop this bloody killing just at the door of the European Union," the French foreign minister, whose country holds the EU rotating presidency, said.
The Finnish foreign minister, who holds the OSCE rotating chairmanship, said he was more optimistic now than yesterday.
"We need a ceasefire and after that we need withdrawal of troops and after that we can move towards peace negotiations," he told BBC World.
He re-iterated President George W. Bush's call for a return to the status quo ante of August 6.
"We will start with a ceasefire; we will work on the humanitarian aid side, because there are people in need on both sides," Stubb said. He added that only then would it be possible to think about a possible peacekeeping format.
"I can not say that it will be ended today, but I am optimistic that in the near future we will come into solution; whether it happens today, tomorrow or day after tomorrow – I do not think anyone knows at this stage," he said. "We have a good start here in Tbilisi and time to move on to Moscow, let's see what they have to say."
The two foreign ministers are due to visit the Georgian town of Gori, close to the South Ossetian conflict zone. The town has been subject to repeated Russian aerial attacks in the last few days.