Tensions have remained high between the two countries following a short conflict in 2008. Hundreds died in clashes over the sovereignty of South Ossetia and Abkhazia -- two breakaway Georgian regions which Russia recognizes as independent countries, CNBC reports.
Kvirikashvili said that several formats of dialog now existed between the two countries, and that there were positive dynamics in terms of trade.
"We are trying to decrease the tensions with Russia in order to allow ourselves to attract investments, because stability and security (are)... the main prerequisites for any investor," Kvirikashvili told CNBC's Hadley Gamble at the World Economic Forum in Davos.
There were still issues, however. Russia was still signing agreements with both South Ossetia and Abkhazia, Kvirikashvili said, something he described as "against all logic."
"But this is where we are," he said. "We will continue a pragmatic approach, we will continue from our side to decrease the tensions, and we welcome, of course, the recent decision of the Russian government to ease the visa regulations for Georgian citizens," he added.
"This was a positive step, and it is appreciated by (the) Georgian government and people."
Asked if he had a message for Vladimir Putin, Kvirikashvili said that, "Russia should honor Georgia's territorial integrity and sovereignty."
"This is the main entry condition to be met by the Russian side in order to start normal relations with Russia," he said.
"Honestly, we don't see enough political will today in (the) Russian leadership to resolve this crisis, but despite all that, we have (a) longstanding tradition of… relations with Russia, and I don't think that we need to scratch out everything," Kvirikashvili added.
"Culturally, Georgians, we are Europeans, we are a European country," Kvirikashvili also said during the interview.
On Friday the Georgian government announced that Kvirikashvili had met with NATO secretary general Jens Stoltenberg while at Davos. The two parties discussed issues relating to Georgia becoming a NATO member, according to the prime minister's press office.
A former foreign minister, Kvirikashvili assumed his role as Georgia's prime minister at the end of last year, after the sudden resignation of Irakly Garibashvili, - concludes the CNBC.