"We've sent a letter of explanation to the English bid officials," Alexei Sorokin, general director of the Russian bid, told Reuters on Wednesday.
On Tuesday, England's bid team lodged a formal complaint with football's governing body FIFA against Sorokin, accusing him of making critical comments about rival bidders in a Russian newspaper.
"It's no secret that London has the highest crime rate when compared with other European cities, and the highest level of alcohol consumption among young people," Sorokin was quoted as saying in the Sport-Express daily earlier this month.
He later said his comments had been "misinterpreted and distorted".
"It wasn't a formal apology because I don't feel like I've broken any rules," Sorokin said on Wednesday.
"I just expressed my regret over the whole thing, it was just a misunderstanding. All of us in the Russian bid team have a great deal of respect for our English colleagues and I'd like to think they respect us as well," he added.
"I hope we can put this matter to rest for good now."
Russia and England are bidding for the 2018 finals along with joint bids from Spain/Portugal and Belgium/Netherlands.
The United States, Japan, South Korea, Qatar and Australia are the candidates for the 2022 tournament.
