He also revealed the announcement of the host cities has been brought forward several months, to October 2012, in order to give the world's largest country more time to prepare for the 32-team football extravaganza.
"After the [outer] Moscow region dropped out last month we still have 13 candidate cities and a total of 15 stadiums," Mutko, who is also a member of FIFA's executive board, told reporters following a joint meeting of LOC and FIFA officials.
"In the next few months we will choose 12 stadiums in 11 cities that would host the tournament."
Mutko declined to name the favourites.
"Every city, be it Moscow [the largest] or Saransk [the smallest] has an equal chance to be selected," he said.
"And no city is guaranteed a World Cup status if it's not ready. Everything must be first class: the stadium, the airport, hotels, roads, all the infrastructure."
FIFA's Secretary General Jerome Valcke was asked about specific problems facing the Russian organisers.
"Honestly speaking, we are more concerned with [2014 World Cup hosts] Brazil at the moment," he said.
TRAFFIC NIGHTMARE
"I've only been to two Russian cities: Moscow and Saransk. The first issue in Moscow is traffic - it's a nightmare.
"But we're talking about 2018 so we have time to try to solve all the problems."
The Russians are building 11 of the 12 World Cup arenas from scratch but Mutko said several of the stadiums should be ready in a year or two.
"St Petersburg should have a brand new 69,000-seat stadium by the end of 2012 while Kazan will open its 45,000-seat arena in early 2013," he said.
"And the Sochi stadium will host the opening ceremony of the 2014 Winter Olympics so it should be ready on time."
Mutko also disputed the cost of renovation at Moscow's 84,000-seat Luzhniki stadium, which would likely host the World Cup final and one of the semi-finals.
Asked if the price of 40 billion roubles ($1.27 billion) was justified, he snapped back: "40 billion? It's way too much, you could build two stadiums for that money.
"I think a new Wembley only cost 30 billion. I think whoever gave this figure must have had other things in mind," said Mutko, who is also Russia's Sports Minister.
