Turkey's proposal was the country's latest effort to promote peace between Georgia and Russia since they fought a war this month over Georgia's separatist republic of South Ossetia.
Babacan hosted Georgian Foreign Minister Eka Tkeshelashvili, two days before he is to meet Russian Foreign Minister Sergei Lavrov in the same city.
Georgia welcomed Turkey's proposal for a Caucasus alliance, Babacan told a joint press conference with his Georgian counterpart Tkeshelashvili. Georgian foreign minister, however, said her country would only consider joining such a group after Russian forces leave his country and fully apply the ceasefire.
Babacan said Turkey saw "Caucasus Stability and Cooperation Platform" as a mechanism through which countries could discuss cooperation opportunities particularly in economy, discuss some concrete measures particularly confidence-building ones, and find solutions to problems.
He added Turkey wanted to see five countries in the platform, and had talks with all those countries.
"I had the opportunity to discuss the proposal in detail with Tkeshelashvili, and I also debated it with Azerbaijan," he said.
Babacan said that he would also discuss the matter with Lavrov during his visit to Turkey on Tuesday.
Russian troops entered Georgia on August 8 to push back a Georgian offensive to retake South Ossetia, which broke away from Tbilisi in the 1990s with Moscow’s backing.
Georgia and Russia accuse each other of having provoked the conflict. Moscow has pulled out most troops after a French-mediated ceasefire agreement but Tbilisi wants all Russian forces to leave the country.
Babacan said Turkey supported its northeastern neighbor's territorial integrity, and added the Caucasian countries had common futures.
He said Turkish-Georgian relations were grounded on a strong basis, adding Baku-Tbilisi-Ceyhan oil pipeline, Baku-Tbilisi-Erzurum natural gas pipeline and Baku-Tbilisi-Kars railway project are the natural products of Turkey's strategic cooperation and neighborly relations in South Caucasus.
"These projects, in fact, have linked the Caspian Sea with the Mediterranean, Caspian basin with Anatolia and the Caspian Sea with the Black Sea," he said.
Babacan also called on everyone to behave calmly after recent tension and disagreements in the region.
"We all know from previous experiences that no one wins in such tensions, and every one will lose something," he said.
Tkeshelashvili warned of a "domino effect" in the Caucasus region and Ukraine after Russia moved troops into Georgia.
"Russia's military hostility against the small state of Georgia could have a domino effect in other countries of the region like Ukraine," she said.
She accused Moscow of an "expansionist policy" and called on the international community to back Georgia's territorial integrity.
The Turkish delegation would also discuss with Armenian officials issues regarding a possible visit of Turkish President Abdullah Gul to Yerevan to watch a football match between Armenia and Turkey, Babacan told the conference.
Armenian President Serzh Sargsyan has invited Gul to watch a football match between the two countries' national teams on Sept. 6 to mark "a new symbolic start in the countries' relations."
Turkish president said Saturday he is yet to make a decision on accepting the invitation. However, Turkey's Prime Minister Tayyip Erdogan said in the same day he wished Gul's visit would bring positive results, hinting that Gul might have actually decided to accept Sargsyan's invitation.
Erdogan also said Babacan would accompany the Turkish President during the trip to discuss relations with Armenia.
Turkey is among the first countries that recognized Armenia when it declared its independency. However there is no diplomatic relations between two countries, as Armenia presses the international community to admit the so-called "genocide" claims instead of accepting Turkey's call to investigate the allegations, and its invasion of 20 percent of Azerbaijani territory despite U.N. Security Council resolutions on the issue.
A warming period had started between two neighboring countries after the presidents exchanged letters after Sargsyan's election victory.