Officials have denied that MI5 held back information from Ms Patel, following allegations that officials lacked confidence in her abilities.
She has also been accused of trying to force out Sir Philip Rutnam, the most senior civil servant in her department.
The pair were both said to be “deeply concerned” by the “false allegations”.
Downing Street has backed Ms Patel, with the prime minister’s official spokesman telling reporters Boris Johnson had “full confidence” in the home secretary.
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A spokesman for Ms Patel and Sir Philip said they were focused on delivering their department’s “hugely important agenda” such as an overhaul of the immigration system, putting more police officers on the streets and combating terrorism.
The statement comes after a source told the BBC there had been no animosity or “blazing rows” between Ms Patel and Sir Philip – who has been the Home Office’s permanent secretary since April 2017 – but they were simply “not the right fit”.
The BBC’s assistant political editor, Norman Smith, said the intervention from a security service source – saying the claims they withheld information from the home secretary were “simply untrue” – was “highly unusual”.
The Home Office said “no formal complaints” had been made about Ms Patel, who has been home secretary since Boris Johnson became prime minister.
Security Minister James Brokenshire told BBC Breakfast there had been “a lot of false stories” circulating about Ms Patel, and security briefings had been continuing as normal.
He added: “I simply do not recognise the commentary and the false accusations and assertions that in so many ways have been swirling around.”
Former Environment Secretary Theresa Villiers also said she was “sick of spiteful briefings against women in high public office”, calling Ms Patel a “highly effective home secretary”.
She told BBC Radio 4’s Today programme she believed there was an element of misogyny to the allegations, adding: “I’m absolutely certain that she’s tough and demanding on her civil servants” but she did not think “anything inappropriate” had gone on with her staff.
The Sunday Times claimed the home secretary has not been receiving the same security and intelligence briefings as her predecessors because MI5 officials do not trust her.
A government spokesman said Ms Patel and MI5 had “a strong and close working relationship, and baseless claims to the contrary are both wrong and against the public interest”.
They added that no information was being withheld from her and she “receives the same daily intelligence briefings as her predecessors”.
The Times reported that a “livid” Ms Patel has asked for an inquiry to be carried out into how the “hostile briefings” about MI5 happened – although Cabinet Office sources said no such request has been made.
The allegations come alongside reports of tensions between the civil service and the government over recruitment and treatment of staff.
The Cabinet Office is recruiting a new civil servant to oversee HR policy for government ministers’ special advisers.
