Migrant communities must be compelled to do more to integrate to help combat the rise of “far-right bigotry”, Tony Blair has warned.

The former prime minister said that successive governments had “failed to find the right balance between diversity and integration”, while the concept of multiculturalism has been misused as a way to justify a “refusal to integrate”.

Blair makes the pointed intervention in a report by his Institute for Global Change, which backs forcing schools to have an intake that reflects local diversity, creating a compulsory citizenship programme for teenagers and toughening enforcement against the perpetrators of hate speech.

It also calls for compulsory citizenship education, a ban on segregated shift patterns and the creation of a new cabinet post created to oversee integration.

“Over a significant period of time, including when we were last in government, politics has failed to find the right balance between diversity and integration,” Blair writes in a foreword to the report. “On the one hand, failures around integration have led to attacks on diversity and are partly responsible for a reaction against migration. On the other hand, the word multiculturalism has been misinterpreted as meaning a justified refusal to integrate, when it should never have meant that.

“Particularly now, when there is increasing evidence of far-right bigotry on the rise, it is important to establish the correct social contract around the rights and duties of citizens, including those who migrate to our country.”

The report backs a new form of “digital identity verification” – a return to Blair’s support for ID cards that caused huge divisions when the idea was pushed by his government and later abandoned. It also backs the idea of increased funding for language tuition and handing asylum seekers earlier access to work.

It comes following an increase in religious or racially motivated hate crimes. According to Home Office data, such crimes increased from 37,417 in 2013-14 to 79,587 in 2017-18. MPs such as Labour’s Naz Shah have linked the increase with support for extreme far-right groups.

However, in remarks likely to attract criticism from migrant rights groups, Blair warns that enforcing greater integration by new arrivals is a crucial part of solving the issue.

Blair writes: “In this report, we make it clear that there is a duty to integrate, to accept the rules, laws and norms of our society that all British people hold in common and share, while at the same time preserving the right to practise diversity, which is fully consistent with such a duty.

“Without the right to, for example, practise one’s faith, diversity would have no content; but without the duty to integrate, ‘culture’ or ‘faith’ can be used as a way of upsetting that basic social contract that binds us together.

“Government cannot and should not be neutral on this question. It has to be a passionate advocate and, where necessary, an enforcer of the duty to integrate while protecting the proper space for diversity. Integration is not a choice; it is a necessity.”

In government, Blair pushed the idea that all communities had a “duty to integrate” into British society, adding that no one could override the values of democracy, tolerance and respect for the law.

“Our tolerance is part of what makes Britain, Britain,” he said in 2006. “Conform to it; or don’t come here.”