Russia's communications minister tweeted that Prime Minister Dmitry Medvedev urged the social media giant's founder to abandon plans to lure away Russian programmers and instead open a research center in Moscow.
A Facebook spokeswoman, who refused to be named because she wasn't authorized to discuss the matter with the media, said the company has no immediate expansion plans for Russia.
Zuckerberg, who ditched his trademark hoodie and jeans for a suit and tie for his meeting with Medvedev, was visiting Russia on a world tour of programming contests to identify new talent.
Russian Web companies often command larger shares of the domestic market than their U.S. counterparts. Facebook has roughly 9 million users in Russia, while domestic clone VK has around 34 million.
Medvedev has cultivated a tech-friendly image since launching his modernization program while president of Russia from 2008 until this May, when Vladimir Putin returned for his third term as president.