The Georgians released a video of Glukhov on Tuesday in which he described why he had deserted and fled to Georgia. The Russian military claimed he was captured in South Ossetia and demand his return.
"We will protect his rights and we are not planning to hand Glukhov over to Russia," Vashadze said. "We know quite well that he will be threatened if we hand the soldier back to the Russians."
The foreign minister said that he had contacted the Swiss ambassador in Georgia, who represents Russia in the country as Tbilisi and Moscow cut all diplomatic relations after the five-day war in August last year.
"We have invited the ambassador of Switzerland so that he can confirm Glukhov's situation in Georgia and to what degree his rights are being protected," the minister said.
He said that Georgia had already contacted the sergeant's parents and invited them to Tbilisi to visit their son.
In the video released on Tuesday, Glukhov explained why he left his division, deployed in Akhalgori, near the South Ossetian border with Georgia. The Russian soldier requested that Georgian President Mikheil Saakashvili grant him political asylum and allow him to live in Tbilisi.
The Georgia Interior Ministry has said it is looking into the possibility of granting Glukhov citizenship.
A Russian Army spokesman, Igor Konashenkov, told RIA Novosti that Glukhov was under moral and psychological pressure and possibly being threatened.
In an interview with journalists in a Tbilisi McDonald's restaurant on Tuesday, Glukhov said he deserted from the Russian Army and wanted to remain in Georgia. He had already called his mother to calm her.