BRUSSELS—Officials from Gazprom OAO and the Russian government traveled to Brussels on Thursday to discuss European Union charges that the Russian energy firm hindered competition and charged unfair prices in Eastern Europe.

The talks, between the EU’s antitrust chief, Margrethe Vestager, Gazprom Deputy Chairman Alexander Medvedev and Russian Deputy Energy Minister Anatoly Yanovsky, were “open and constructive,” according to the European Commission, the bloc’s top antitrust authority.

Mr....