Earlier, Athens asked Moscow to loosen measures taken in 2014 on the import of Greek agricultural goods to Russia in response to EU sanctions against the country for its alleged role in the Ukrainian crisis.
"The issue isn't about Greece, this is an overall issue, everyone suffers from sanctions, both those who impose them and those who respond to them. This is not Russia's way," Meshkov said.
The European Union, alongside the United States, has imposed several rounds of sanctions on Russia, accusing Moscow of meddling in Ukraine's internal affairs and escalating the crisis in the country.
In retaliation to the western sanctions, in August 2014, Moscow introduced a one-year food embargo, banning a range of food items from the EU, the United States, Canada, Australia and Norway.
On Monday, Russian Economic Development Minister Alexei Ulyukayev said, however, that Russia was looking for ways to ease the food embargo for Greece and Hungary that would not contradict World Trade Organization (WTO) regulations.