Extremism "anywhere in society is a serious problem" that is being tackled by ministers across departments, a Government spokesman said.
The message was sent out after an exchange between Theresa May and Michael Gove over the handling of the threat of Islamist extremism in schools in Birmingham.
There is no difference between the Education Secretary and the Home Secretary, who are both working energetically together to tackle the challenge posed by any form of extremism.
The spokesman added that the work of the Prime Minister's Extremism Taskforce demonstrated action being taken by government.
Speaking to BBC Radio 4's World At One, Conservative Party chairman Grant Shapps denied that the letter from May to Gove demonstrated a fight within the cabinet. He said:
It's somehow being suggested by commentators that this is somehow a big bust-up. In fact, I see Michael and Theresa work together all the time.
More top news
Feeling warm in the sunshine
Speaking after the Westminster attack, Brad Smith exclusively told ITV News that Microsoft will only hand over data when legally compelled.
Kurt Cochran and his wife Melissa had been visiting London from the US to celebrate their 25th wedding anniversary and were due to fly home.