Speaking at a European Parliament session in Strasbourg, Saakashvili said: "I have no intention of using the European Parliament's podium to escalate tensions with Russia, and I am calling on the Russian leadership to get back to the path of dialogue with Georgia."
He said he would not want to see Georgia's relations with Russia worsen "beyond repair."
Russia cut transportation and postal links with Georgia and deported several hundred Georgian migrants after the brief arrest in September of four Russian army officers on espionage charges.
State-controlled natural gas monopoly Gazprom said it will more than double the price of its gas deliveries to Georgia.
Earlier this year, Russia banned the import of Georgian mineral water and wines.
The U.S.-educated Saakashvili, who came into power on the back of a "rose" revolution in 2003, claims that Russia still regards sovereign Georgia as its own backyard and seeks to punish his country for ambitions to join NATO and the European Union.
"Georgia is being punished for its desire to integrate into Euro-Atlantic structures, but there is no way the process will stop," he said.
"Georgia's European vector is not a goal unto itself - this is our choice and our policy. In this context, strained relations with Russia are a temporary phenomenon, and our relations will [eventually] get back to normal."
Earlier on Tuesday, the European Union signed agreements with Georgia and two other post-Soviet South Caucasus states, offering them economic assistance in exchange for a commitment to market reform.
Along with a promise of easier access to EU markets, the "European Neighborhood" accords envisage cooperation in sectors such as transportation, energy, environment, public health and education, yet stop short of offering EU membership.
The EU hopes the accords will help the South Caucasus nations normalize their relations with Russia, as well as to resolve "frozen conflicts" in the region, notably Georgia's conflict with its breakaway provinces of Abkhazia and South Ossetia.
Brussels has refused to recognize Sunday's independence referendum in South Ossetia, where the vast majority of the population spoke in favor of seceding from Georgia.
The tiny province broke away from Georgian rule in a bloody war in the early 1990s, but Saakashvili's government is determined to bring it and Abkhazia back into the fold.
