Education Secretary Michael Gove has denied being at war with Theresa May, saying the Home Secretary is doing a "fantastic job".
Asked if she was too soft on Islamic fundamentalism, Mr Gove told reporters: "No absolutely not, she's doing a very fine job."
The Prime Minister has stepped in after an exchange between ministers over the handling of alleged Islamist extremism in Birmingham schools.
A Downing Street source said David Cameron was "keen to establish the facts" after Theresa May wrote to Michael Gove questioning why his department had not acted on warnings of a supposed plot by Islamist extremists.
May's letter inquired about evidence that the Department for Education knew of the 'Trojan Horse' allegations in 2010 and asked: "If so, why did nobody act?"
As the letter emerged the pair took the unusual step of issuing a joint statement insisting they were "working together" on the issue.
From the Government's point of view, too much of today's news agenda has been taken up discussing the spat between Theresa May and Michael Gove.
Theresa May is much-beloved on the Tory right, seen as a big success as Home Secretary and is leading the current polls for potential future leader of her party.
Michael Gove is very close to David Cameron and is leading - in Tory terms - critical education reforms.
They're both effectively unsackable members of the Cabinet.
If that wasn't the case, I think David Cameron would be thinking about sacking them for this extraordinary case of ill-discipline at a terrible time for the Government.
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.
A spokesperson for Michael Gove and Theresa May said:
The Department for Education and the Home Office take the problems in Birmingham schools and all issues relating to extremism very seriously.
Michael Gove and Theresa May are working together to ensure we get to the bottom of what has happened in Birmingham and take the necessary steps to fix it.
A source close to the Education Secretary said: "Michael Gove thinks Theresa May is a superb Home Secretary.
"We will continue to work well with the Home Office and other government departments to combat extremism in all its forms.
Ofsted will publish their findings next week and Peter Clarke will publish his report in July."
Responding to concerns raised by Home Secretary Theresa May about the Department for Education's efforts to prevent Islamic extremism in schools, a spokeswoman said it was "investigating all evidence."
In a statement the department said: "The allegations made in relation to some schools in Birmingham are very serious and we are investigating all evidence put to us in conjunction with Ofsted, Birmingham City Council and the police.
"It is absolutely vital these investigations are carried out impartially, without pre-judgment."Ofsted has inspected a number of schools in the light of recent allegations and will report to the Secretary of State shortly.
"Retired senior police officer Peter Clarke has been asked by the Secretary of State to make a full inquiry into Birmingham schools and will report back this summer."
In an extract from the letter Theresa May wrote to Michael Gove raising questions about his department's treatment of Islamic extremism in schools, she asks directly "why did nobody act?"
How did it come to pass, for example, that one of the governors at Park View was the chairman of the education committee of the Muslim Council of Britain?
Is it true that Birmingham City Council was warned about these allegations in 2008?
Is it true that the Department for Education was warned in 2010? If so, why did nobody act?
I am aware that several investigations are still ongoing and those investigations are yet to conclude.
But it is clear to me that we will need to take clear action to improve the quality of staffing and governance if we are to prevent extremism in schools.
Home Secretary Theresa May has appeared to question Michael Gove's actions over curbing extremism in schools, in a letter to the Education Secretary.
May wrote to Gove to ask about evidence that the Department for Education knew about claims of extremism in schools in Birmingham as far back as 2010 and asked: "If so, why did nobody act?"
She raised concerns about the "inability" of local and central government to tackle the problem following the allegations of extremism in Birmingham schools.