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Jessica Parker
BBC political correspondent
Around a dozen Tory MPs, including ministers, have complained to the chief whip about Suella Braverman's recent speech on immigration and refugees.
Some have told the BBC her remarks were offensive, divisive and inaccurate.
As first reported by The Times, they raised concerns after the home secretary said being gay or a woman should not entitle people to protection as a refugee.
She later said some people "purport" to be gay, to try to "game the system".
Ms Braverman has been approached for comment.
The MPs have spoken to the BBC on condition of anonymity.
"Why do you need to single out one section of people?" asked one.
It is not the first time, MPs say, that there have been concerns about the home secretary's tone.
It's unclear exactly what will happen as a result of the complaints but it is expected the government chief whip - who is in charge of MP discipline - will relay the concerns to the prime minister.
Sources have also suggested Ms Braverman may speak personally to some of those who are unhappy.
Downing Street has said it signed off the home secretary's speech to a Washington DC think tank.
Earlier this week, one Conservative MP told the BBC: "The danger is that unless the PM deals with her [sacks her], it reflects poorly on him."