The Prime Minister was "keen to establish the facts" behind the turf war between Theresa May, the Home Secretary, and Michael Gove, the Education Secretary, a No 10 source said.
Ms May has suggested her Scots-born colleague's department had failed to deal with warnings of a plot by hardline Islamists to seize control of classrooms in several Birmingham schools.
Her letter questioning its response to the so-called "Trojan Horse" plot was said to have come after the pair clashed over the Education Secretary's concerns that the Home Office was doing too little to confront extremism at its roots.
A Home Office source hit out at Mr Gove's department, saying it was "responsible for schools, the Home Office is not. They have got a problem and are trying to make it someone else's problem."
Meantime, Crispin Blunt, a former Conservative Prisons Minister, accused Mr Gove of promoting "neocon" ideas that could encourage moderates to move towards Islamist extremism.
Tensions between the two Secretaries of State first broke out last year when he accused her of promoting herself as a future party leader.
As reports emerged of the dispute, the pair took the unusual step of issuing a joint statement insisting they were "working energetically together" on the issue of extremism in schools.
Grant Shapps, the Conservative Party Chairman, sought to play down the differences, insisting such exchanges of views were "a perfectly normal part of government".