David Cameron has rebuked Nigel Farage after the Ukip leader blamed a “fifth column” in European countries for the Charlie Hebdo terrorist shootings by Islamist extremists.

The prime minister said it was wrong to make political arguments so soon after the “appalling events” in Paris, and Labour’s Dame Tessa Jowell accused Farage of making “sickening comments”.

Speaking at an event on Manchester to promote the government’s plan to create an English “northern powerhouse”, Cameron said the terrorists were wholly responsible for the attack as he distanced himself from Farage who blamed the shootings on a “really rather gross policy of multiculturalism” in Europe.

Cameron said: “With the appalling events in Paris still so fresh in people’s minds and with people still struggling for their lives who have been injured, I think today is not the day to make political remarks or political arguments. Today is the day to stand four square behind the French people after this appalling outrage and simply to say that we will do everything we can to help them hunt down and find the people who did this.

“The cause of this terrorism is the terrorists themselves. They must be found, they must be confronted, they must be punished.”

Farage told LBC radio earlier that Britain and other EU countries were paying the price for decades of multiculturalism, which he said, had discouraged integration. He also said the Rochdale child abuse scandals showed that authorities had turned a blind eye for fear of being racist.

The Ukip leader said: “What should have been done is we should have had a controlled immigration policy and made sure we did full checks on everybody who ever came to this country from anywhere – and that applies to everyone else. We in Britain, and I’ve seen some evidence of this in other countries too, have a really rather gross policy of multiculturalism. By that, what I mean is that we’ve encouraged people from other cultures to remain within those cultures and not integrate fully within our communities …

“I don’t think anyone can pretend there is a quick fix to this. We have, I’m afraid, and mercifully it’s small, but we do have a fifth column within our countries.”

He continued: “And added to that, we have turned a blind eye. You’ve only got to look in the north of England and the sexual grooming of young children to see admissions from public figures that they didn’t bother to turn over the stone when they heard rumours of things going wrong, for the fear they might be thought to be racist. So we have made some awful mistakes, but we are where we are.

“On a cultural level, what price anybody who is a standup comic, a cartoonist, a newspaper columnist, who wants to say something critical about Islam at all?”

Cameron said political leaders should focus on highlighting common values across Europe. He said: “The only other thing we should say today is that, as countries in Europe, we share certain values – values that are not incidental to our success, values that are a key part of our success as free and open societies and successful economies.

“Those values include freedom of speech, the right to disagree, the right to argue in public, the right to have a government under the rule of law, the right to have a tolerant society with a strong democracy. Today is the day to make those arguments and those points and, I would argue, not much more than that.”

Cameron said it would be wrong for him to dictate to the press after he was asked whether newspapers should show their support for Charlie Hebdo by publishing its cartoons. “In terms of the values displayed by our media organisations, I don’t think it would be right for a politician to lecture them about that. We have a vibrant, exciting, passionate, disputatious, sometimes infuriating press. Long may that be the case.”

The prime minister’s criticism of Farage was echoed by Theresa May, who said the Ukip leader’s comments were irresponsible. The home secretary confirmed that the Home Office had taken the precautionary step of raising security at seaports.

May told BBC News: “I think it is irresponsible to talk about a fifth column. We should all be working across society to ensure that we deal with and eradicate extremism wherever it exists.”

Labour’s Jowell said the murder of innocent people was “criminal, plain and simple”.

Nick Clegg said on his weekly LBC phone-in: “I’m dismayed, really, that Nigel Farage immediately thinks, on the back of the bloody murders that we saw on the streets of Paris yesterday, that his first reflex is to seek to make political points.

“If this does come down to two individuals who have perverted the cause of Islam to their own bloody ends, let’s remember the greatest antidote to the perversion of that great world religion, Islam, are law-abiding British Muslims themselves.

“And to immediately somehow suggest that many, many British Muslims, who I know feel fervently British but also are very proud of their Muslim faith, are somehow part of the problem, rather than part of the solution, I think is firmly grabbing the wrong end of the stick.”