The Muslim Council of Britain has raised objections to a letter from the communities secretary, Eric Pickles, asking Muslim leaders to “explain and demonstrate how faith in Islam can be part of British identity”.

In a letter sent to more than 1,000 Islamic leaders (pdf), Pickles stressed that he was proud of the way Muslims in Britain had responded to the Paris terror attacks, but added that there was “more work to do” in rooting out extremists and preventing young people being radicalised.

The letter co-signed with communities minister and Muslim peer Lord Ahmad, Pickles told British mosques that radicalism “cannot be solved from Whitehall alone”.

Harun Khan, deputy secretary general of the council, said: “Is Mr Pickles seriously suggesting, as do members of the far right, that Muslims and Islam are inherently apart from British society?”

He said he was writing back to Pickles to demand an explanation for the assumptions that appeared to be in the letter.

In the letter Pickles wrote: “You, as faith leaders, are in a unique position in our society. You have a precious opportunity, and an important responsibility, in explaining and demonstrating how faith in Islam can be part of British identity.

“We believe together we have an opportunity to demonstrate the true nature of British Islam today. There is a need to lay out more clearly than ever before what being a British Muslim means today: proud of your faith and proud of your country. We know that acts of extremism are not representative of Islam, but we need to show what is.

“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.

“We must show them the multitude of statements of condemnation from British Muslims, show them these men of hate have no place in our mosques or any place of worship, and that they do not speak for Muslims in Britain or anywhere in the world.

“Let us assure you that the government will do all we can to defeat the voices of division, but ultimately the challenges of integration and radicalisation cannot be solved from Whitehall alone. Strong community-based leadership at a local level is needed.”

The letter said: “British values are Muslim values”, and the country would be “diminished” without Islam and its “message of peace and unity”.

“Every day, mosques and other faith institutions across the country are providing help for those in need, and acting as a centre for our communities.

“It is these positive contributions that are the true messages of faith and it is these contributions that need to be promoted.”

Ahmad said the council’s response was “disappointing”, adding that perhaps Khan was not clear what the letter said.

He said that “the letter could not have been more explicit” that the government regarded Muslims as part of British society, adding the letter was designed to reassure the Muslim community. He insisted the best way to deal with the language of hate was education and a coming together.

“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,” he said on BBC Radio 4’s Today programme on Monday.

Lord Sacks, the former chief rabbi, said he could understand the reason Muslim leaders might be asking why the government was putting the blame on the community when radicalised Islam was a global phenomenon transmitted by the internet and social media.

He said he was sure the letter was” incredibly well intentioned”, but it “suggested the Muslim community within Britain contained its own radicals and the truth is that Islamism, like all modern global political movements, is actually a global phenomenon transmitted by the internet and transmitted by social media, so I would be surprised if the Muslim community did not say: ‘You are asking of us something that is not actually under our control.’”

But he said he did not believe the Muslim community had done enough to ensure the teaching in its schools and mosques emphasised the need to integrate with British society in the same way as the Jewish community had in the 19th century.

Explaining how much had been done to integrate Jewish society in the UK through teaching in seminaries, he said: “I don’t think that has been done with other ethnic minority communities. Radicalised imams have in the past been preaching a message of hate.”

He added: “We have been in denial about the depth and strength of this problem for a very long time.”

He admitted that fear of attacks in the Jewish community was “at an all time high so far as my lifetime is concerned.

“At the same time the most recent survey shows the overwhelming number of Jews here feel safe and Britain remains one of the most tolerant societies on Earth.

He insisted the Jewish community was well prepared and “this is well under control”.

News of the letter emerged as the Metropolitan police announced that they had increased security around their buildings and bolstered the number of firearms officers available.

The home secretary, Theresa May, also promised to increase the government’s efforts to tackle the terrorist threat and a “chilling” rise in anti-semitism.