Deputy chief constable Mark Roberts, who is Britain's most senior police football officer, made the comments following the death of a policeman at Spartak Moscow's Europa League match with Athletic Bilbao on Thursday.
Roberts has advised England fans to consider the behaviour of Russian fans before deciding whether to travel to the World Cup.
"We have an ongoing dialogue with the Russian police and will seek their views on how Thursday night's events may influence their approach," Roberts told The Telegraph.
"Our thoughts are, of course, with the family, friends and colleagues of the Basque officer. Scenes such as last night have no place in society, let alone football.
"This will, of course, cause concern for those England fans planning to travel to the World Cup and the behaviour of Russian fans needs to be a factor in deciding whether to go there or not."
Roberts, who oversaw Britain's policing at Euro 2016 in France, has been tasked with doing so again in Russia this summer.