"They will be safe in Russia," Alexander Yakovenko told a press conference at the London embassy.
All the necessary measures are being taken, and the British special authorities are in contact with the special Russian authorities to provide security.
"It's regular precautions that we are doing with every single country.
"I am sure that there will be full security, and by the way there will be a visa free regime for those who are coming to Moscow.
"They will be the guests of Russia."
The comments came amid an escalating war of words between Russia and Britain over the poisoning of a Russian former double agent on British soil on March 4. Moscow denies involvement in the case.
British Foreign Secretary Boris Johnson on Wednesday called for Russian guarantees over the safety of England fans at the World Cup in June and July.
Johnson also said President Vladimir Putin would exploit the 2018 football World Cup in Russia as Nazi dictator Adolf Hitler had done with the Berlin Olympics.
Johnson agreed with an MP who suggested, "Putin is going to use it in the way Hitler used the 1936 Olympics", as a propaganda exercise.
"I think the comparison with 1936 is certainly right," the minister replied, envisaging Putin "glorying in this sporting event".
Yakovenko condemned Johnson's comparison.
"I'm authorised to say that Moscow considered these kind of statements... in any way unacceptable and totally irresponsible," he said.
"The British government is free to make a decision about its participation in the World Cup but nobody has the right to insult the Russian people who defeated Nazism... by comparing our country to Nazi Germany.
"We do not think British war veterans, including those of the Arctic Convoys, would share this opinion," he said, referring to World War II oceangoing convoys which sailed from the United Kingdom, Iceland, and North America to northern Soviet ports.