David Cameron has contradicted the pope over whether it is right to react with violence against insults to religious beliefs.

The prime minister told a US news programme that it was wrong to “wreak vengeance” if someone insulted your faith.

Speaking to journalists on a plane last week, Pope Francis had said insulting others’ faith was a step too far.

His explanation that those who provoked others by insulting their religious beliefs should expect violence came days after Islamist terrorists killed 12 people at the offices of French satirical newspaper, Charlie Hebdo, before killing four more Jewish people at a kosher supermarket. The killers claimed allegiance to Islamic State (Isis) and al-Qaida in Yemen.

During an impromptu press conference, the pope gestured to one of his officials, and said: “If my good friend Dr Gasparri says a curse word against my mother, he can expect a punch. It’s normal. You cannot provoke, you cannot insult the faith of others. You cannot make fun of the faith of others.”

Cameron was asked about the pope’s remarks in an interview with the CBS news programme Face the Nation, broadcast on Sunday. He said: “I think in a free society, there is a right to cause offence about someone’s religion. I’m a Christian; if someone says something offensive about Jesus, I might find that offensive, but in a free society I don’t have a right to wreak vengeance on them. We have to accept that newspapers, magazines, can publish things that are offensive to some, as long as it’s within the law. That is what we should defend.”

The PM was also asked about the current terrorist threat, and said that it was severe and that an attack was highly likely. He said the nature of the threat “has changed and altered, but it’s still based on the fundamental problem of a poisonous death cult narrative which is the perversion of one of the world’s major religions.”

The interview was pre-recorded in the US before Cameron flew back to the UK following talks with Barack Obama. Last August, Obama was criticised for saying “we don’t have a strategy yet” for tackling Islamic State. Cameron told CBS there was now a strategy.

“I think the reason some people are concerned about this strategy is that perhaps we haven’t said enough about how long it is going to take to work. If we take the issue of Islamist extremist terrorism coming out of Iraq and Syria, it is going to take a very long time to deal with this, because in the end the only answer to these terrorists will be strong, proper government in Iraq, with strong, proper Iraqi security forces.

“The same applies in Syria. I think the secretary‑general of the UN put it very well when he said a missile can kill a terrorist, but it is only good governance that can kill terrorism. So what we’re engaged in is a very long struggle where we’ll have to show real perseverance.”