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
Pregnant women and new mothers are suffering growing discrimination at work, according to a new report.
More than one in four Britons aged 55 and over financially support their child or other dependents to get on to the property ladder.
Known as 'spice' and 'black mamba', the so-called legal high is suspected of contributing to deaths in male and female institutions.