Hodgson, who has two years left on his contract, said following the Uruguay defeat that he would not resign, and on Friday Dyke gave him his full backing.
"We're supportive of Roy Hodgson, we've asked him to stay as manager," Dyke told reporters.
When asked by Sky Sports News if he felt Hodgson would remain in his job until the end of his contract at the 2016 European Championships, Dyke added: "That is the view of myself, of everybody else here (in Brazil) and of others in the FA."
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- Roy Hodgson
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