"As a dad and as a human being, do I think we should have tough penalties when football players behave like this? Yes, I think we should," Cameron told BBC Radio 5 Live on Friday.
Suarez, Liverpool's top scorer this season, was banned by the FA on Wednesday for biting Chelsea defender Branislav Ivanovic during a Premier League match at the weekend and has until Friday to decide whether to appeal the decision.
Liverpool manager Brendan Rodgers has criticised the FA over the length of the ban and said comments made by Cameron and others earlier in the week may have influenced the panel at Suarez's hearing.
"There is no doubt that, if you have these high-profile figures making those sorts of statements, there will be bias," Rodgers was quoted as saying by British media on Friday.
In response, Cameron said: "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."
"The FA make the decision, they are entirely independent and that is the way it should work."
An angry Rodgers also accused the FA of throwing Suarez out with the rubbish and said he would understand if the Uruguayan wanted to quit the Premier League.
"He is a player who fell well below the standards of this football club at the weekend but that doesn't mean he should be thrown to the garbage. Which is what has happened from a lot of people," Rodgers said.
"Unfortunately for him he made a mistake and he's got a sanction which I don't believe fits with what he did."
"I understand if he felt he couldn't carry on," Rodgers added. "One hundred percent.
"His two passions are his family and Liverpool Football Club. He has traits that are part of his make up and I genuinely think he is trying to adapt but, each time he takes a step forward, we find ways to beat him with a stick and strike him down.
"I can understand if he felt like leaving in a moment of reflection."
Suarez, who accepted the FA's charge of violent conduct, apologised to Serbian Ivanovic and was fined by Liverpool earlier in the week.
The 26-year-old was banned for eight matches last season for racially abusing Manchester United's Patrice Evra and received a seven-game ban from the Dutch FA for biting an opponent while playing for Ajax Amsterdam in 2010 shortly before he joined Liverpool.
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