"It's already a great success," Sorokin told reporters at Moscow's Luzhniki stadium after Russia beat Spain 4-3 on penalties to make it to the quarter-finals.
"We have had lots of positive reactions from the different teams, fans and delegations. It's going well. For now, things are good."
Ahead of the tournament, there were fears that racism and hooliganism could tarnish the World Cup, which Russia is hosting in 11 cities including Moscow, St. Petersburg and Sochi.
But since the start, there have been no recorded cases of racism and the fears about hooligan violence have not materialised. [nL8N1TV61F]
Sorokin said the Russian team's unexpected success at the tournament had been a contributing factor to the World Cup's appeal.
"It's good that our team remains in the competition," he said of the hosts, who entered the tournament as the lowest-ranked team. "There is a lot of interest."
Russia will face either Croatia or Denmark in Sochi on Saturday in the quarter-finals. The two sides were tied 1-1 after 90 minutes of their round-of-16 match on Sunday and going into extra time.
(Reporting by Gabrielle Tétrault-Farber; Editing by Clare Fallon)
