David Cameron today warned Muslim leaders they had 'a problem' if they objected to being asked to do more to tackle Islamist extremism.

The Prime Minister said letters sent to mosques were 'reasonable, sensible and moderate' and ministers were 'absolutely right' to insist everybody had a responsibility to fight radicalisation.

It came after the Muslim Council of Britain accused the Government of 'ratcheting-up tensions' and adopting the language of the far-right.

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David Cameron, speaking in Ipswich, Suffolk, this morning, insisted Muslim leaders they had 'a problem' if they objected to the Government's demand for them to do more to tackle Islamist extremism

More than 1,100 imams and Islamic leaders have been sent a Government letter urging them to show 'men of hate' that they have 'no place' in Britain's mosques 'or any place of worship'.

In the letter, Communities Secretary Eric Pickles and minister Lord Ahmad write: 'We must show our young people, who may be targeted, that extremists have nothing to offer them.

'We must show them that there are other ways to express disagreement – that their right to do so is dependent on the very freedoms that extremists seek to destroy.'

The letter ends: 'We welcome your thoughts, ideas and initiatives on how to ensure that Islam's true message of peace triumphs over those who seek to divide our communities.'

But some Muslims have expressed anger at the ministers' challenge to show how Islam can be part of British identity.

After the letter emerged this morning, the Muslim Council of Britain said it wanted Mr Pickles to clarify his request and asked if, like 'members of the far right', he was suggesting that Islam is inherently apart from British society.

Deputy secretary-general Harun Khan said: 'We will be writing to Mr Eric Pickles to ask that he clarifies his request to Muslims to 'explain and demonstrate how faith in Islam can be part of British identity'.

'Is Mr Pickles seriously suggesting, as do members of the far right, that Muslims and Islam are inherently apart from British society?'

The letter was sent by Communities Secretary Eric Pickles and minister Lord Tariq Ahmad of Wimbledon

Muslim commentator Mohammed Ansar went further, tweeting: 'Ridiculous and unhelpful intervention from the Communities Secretary, Eric Pickles this morning, by asking all Muslims to prove themselves.

'Government ministers, rather than ratcheting-up tensions and fuelling the fifth column narrative, should be looking to unite communities.'

But asked about the criticism this morning, Mr Cameron insisted the letter was ‘reasonable, sensible and moderate’ and suggested that anyone opposing it ‘really has a problem’.

Answering questions after a speech in Ipswich, the Prime Minister said: ‘I think it is absolutely right to write this letter, to say that we all have a responsibility to fight extremism.

‘Anyone who reads this letter - and I've read the letter - will see that what he is saying is that British Muslims make a great contribution to our country, that what is happening in terms of extremist terror has nothing to do with the true religion of Islam.

‘It's being perverted by a minority who have been radicalised. But everyone needs to help with dealing with this problem of radicalisation.

‘Anyone, frankly, reading this letter, who has a problem with it, I think really has a problem. I think it is the most reasonable, sensible, moderate letter that Eric could possibly have written.

‘Frankly, all of us have a responsibility to try to confront this radicalisation and make sure that we stop young people being drawn into this poisonous fanatical death cult that a very small minority of people have created.’

Finsbury Park Mosque in north London has attempted to tackle the extremists which once worshipped there

The letter was published after Mr Pickles and Home Secretary Theresa May held up signs reading 'I am Jewish' during a Board of Deputies of British Jews meeting yesterday

Mr Cameron's intervention came after Lord Ahmad had earlier rejected the criticism and insisted the letter was clear.

He told Radio 4's Today programme: 'Within the letter there is an explicit paragraph that says British values are Muslim values. You can't be more explicit than that.'

He added: 'Perhaps he wasn't clear in what the letter said but if you have seen a copy of the letter ... it has been pretty explicit that we want to work together with the Muslim community.

'This was about reassurance, it was about recognising, as Theresa May said only yesterday, that a Britain without Muslims, a Britain without Jews, Hindus, would not be the Britain we want to see.'

The letter slams far-right groups like the English Defence League (pictured), but some Muslims say ministers appear to use the same language as such groups by suggesting British and Muslim identity is distinct

Mr Pickles has previously written to Muslim leaders to offer support after arson attacks on mosques by far-right groups, but the latest letter is the first time he has challenged them to tackle extremism.

The letter emerged the day after the Metropolitan Police announced it is reviewing how to keep its officers safe amid fears of a terror plot to kidnap or kill a policeman or woman.

Home Secretary Theresa May also promised to increase the Government's efforts to tackle the terrorist threat and a 'chilling' rise in anti-Semitism.