A trip to McDonald's, a photo shoot on Red Square, and a chummy meeting with one of his biggest fans – it's all in a day's work for Facebook's chief executive, Mark Zuckerberg, who met Dmitry Medvedev, the Russian prime minister, on Monday during a visit to Moscow.

Shedding his usual hoodie for a suit and tie, Zuckerberg exchanged easy grins with the famously tech-loving premier on a visit to his official residence outside Moscow. Medvedev could barely contain his excitement at meeting the co-founder of the world's largest social network. "I have a Facebook page myself," he told his guest.

Zuckerberg was in Moscow to boost Facebook's presence in Russia, where it competes with local social networking sites. He was also due to attend a programming symposium in a bid to attract Russians to work for his firm.

Not all Russians were happy with the visit. Oleg Kozyrev, a prominent opposition blogger, launched a Facebook group called "Zuckerberg, don't be friends with a dictator!", urging the American to meet "not with officials who jail Russian bloggers and create laws on internet censorship, but with bloggers, who suffer from these laws".

Zuckerberg did not meet Vladimir Putin, Russia's powerful president, who claims he does not use the internet.

Social networking sites, including Facebook, have been key to organising the street protests that have swept Moscow since Putin announced he was returning to the Kremlin.