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
As Big Ben falls silent for four years of renovation work, why not test your knowledge of the iconic London landmark?
Female football fans were asked to show their bras to stewards during security searches, a supporters' group has said.
Rain in the Northwest, drier elsewhere