Former England defender Sol Campbell warned supporters to stay away from the tournament because of the threat of racism and violence.
But former England captain Beckham claimed fans would not be put off following the national team.
He said: "Our fans will do what they want. They are passionate about watching England play and watching England perform and win. In the years I have played for England and seen them travel, there are no fans that travel like us.
"They just need to stay safe. It is as simple as that. We have had it in most competitions that I was involved in.
"There was always talk about our fans and whether they were going to be safe. At the end of the day you are not going to be able to stop fans travelling but everybody has to be sensible."
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Beckham's focus this summer is on trying to win a place in Great Britain's Olympics squad, but he insisted he was not fretting over his inclusion.
The 37-year-old, an ambassador for the Games, is bidding to be one of three over-age players in coach Stuart Pearce's squad.
The Los Angeles Galaxy player told This Morning: "I'm not nervous because I think at the end of the day I'm going to be here no matter what.
"Obviously I've been an ambassador for the Olympics and the Olympic bid since we got it back in Singapore and it's something I've been very proud to be a part of.
"Being part of Seb's (Sebastian Coe, chairman of the London 2012 Organising Committee) team that has brought this amazing event to the east end of London where I'm from, I'm very proud of that.
"But obviously I'd love to perform, I'd love to play, I'm very proud to have played for my country 115 times and obviously been captain of the country for quite a few games and quite a few years. I'd love to be involved, but we'll see."