President Barack Obama has called on Americans to "reach out" to their Muslim neighbours and even visit a mosque to break down stereotypes.

He criticised a tendency to blame terror acts such as 9/11 and the more recent atrocities in Paris and San Bernardino on the broader Muslim community.

Many Muslim Americans are worried because threats and harassment against their community are increasing, he said. "We've seen Muslim Americans assaulted, children bullied and mosques vandalised, and we've heard shameful political rhetoric against Muslim Americans that has no place in our country."

He was writing for Religion News Service after his speech to the Islamic Society of Baltimore was criticised by conservative commentors such as Breitbart and Pamela Geller.

He said: "Generations of Muslim Americans have helped build our country. They're the teachers who inspire our kids, and the nurses and doctors whom we trust with our health. They're the champions we cheer for – from Muhammad Ali to Kareem Abdul-Jabbar. They're the police and firefighters who keep us safe, and the men and women in uniform who have fought and bled and died for our freedom."

The attacks on Muslims tear "at the very fabric of our nation", he argued, describing Islam as having a "tradition of peace, charity and justice".

The President said: "Americans of all faiths can reach out to their Muslim American neighbors – perhaps even visit the nearest mosque – to help break down stereotypes and build understanding."

America could never be at war with Islam, he added.

"So we should never play into terrorist propaganda or suggest that all Muslims, or Islam itself, is the problem. That betrays our values. It alienates Muslim Americans. It helps our enemies recruit. It makes us all less safe."

He also called on Muslims to push back against extremist ideologies.

"This is not some clash of civilisations between the West and Islam; it's a struggle within Islam, between the peace-loving majority and a radical minority."