The Uruguayan is fed up of apologising for his bite on Chelsea defender Branislav Ivanovic, which the PM described as an "appalling example to young people in our country"
The striker has refused to commit his future to Liverpool amid rumours that Real Madrid are interested in making an offer for the striker, and has grown increasingly tired of the media attention he receives in England.
Suarez was banned for 10 games for the incident, and has responded to Cameron’s views by insisting he does not need to offer any more apologies.
"Some minister of something, I don't know what, said I don't know what about me, that Suarez is I don't know what to the kids, to his son," he said in a press conference.
"He should care for the English people, he should try to do his job. I won't ask for more forgiveness."
Cameron initially told BBC Radio 5 Live: "I made my own views clear, just as a dad watching the game.
"I have a seven-year-old son who loves football, loves watching football and when players behave like this, it sets the most appalling example to young people in our country.
"As a dad and as a human being, do I think we should have tough penalties when football players behave like this? Yes."