Labour claim Ms Rudd is “hanging by a thread to shield the Prime Minister” after she was forced to apologise for a series of blunders over migrant removal targets.
The Home Secretary has been accused of not telling the truth in Parliamentover the issue.
Colleagues came to her defence on Saturday, with Justice Secretary David Gauke telling Sky News he was confident Ms Rudd had not intended to mislead anyone over whether she knew about migrant removal targets.
He said: “She gave an answer that wasn’t accurate, she wasn’t trying to mislead.
“Amber is a very good Home Secretary.
“She has done excellent work… There are a whole set of reforms she has developed.
“She does a really good job.”
Environment Secretary Michael Gove said she was “a highly talented and highly effective minister”.
“When documents that should be placed in front of a Home Secretary aren’t then placed in front of a Home Secretary, that is sad, that is regrettable,” he told the Today programme.
“But she was very clear both in her apology and also in the fact that this specific document wasn’t placed in her box, wasn’t brought to her attention.”
He also accused Labour of trying to “weaponise” the Windrush issue.
Britons who legally moved to the UK from Commonwealth countries in the decades following the Second World War were called the Windrush generation after a ship carrying workers from Caribbean islands in 1948.
The scandal evolved after it emerged that some have faced difficulties in accessing public services and been threatened with deportation.
Labour MP Jess Phillips told The Big Issue: “I actually feel for Amber Rudd because she has had to clear up the mess that has been left by Theresa May.”
She added: “I’m not sure that Amber Rudd resigning would make all that much difference, especially when I think she is more liberal than she is being allowed to show.”
The Labour Party has said Ms Rudd is being kept in her job to protect Theresa May, who was the architect of the “hostile environment” strategy for illegal immigrants when she was home secretary in David Cameron’s government.
Leader Jeremy Corbyn said Ms Rudd was in a “deeply embarrassing situation” and that he “absolutely” believed she should resign.
He told Sky News: “Both the Prime Minister and the Home Secretary were told in 2014 that the legislation they were passing was very dangerous and would put the Windrush generation in a very precarious situation.
“That was ignored.
“They should think for a moment of the stress that often older people have gone through who have worked their whole lives in this country, considered themselves to be full British citizens – which is exactly what they are – and they should be treated with the dignity and respect as every other citizen should be treated.”
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Shadow home secretary Diane Abbott told BBC Radio 4: “I am just surprised that she doesn’t seem to take the issue seriously enough to offer her resignation.”
Downing Street has said Ms Rudd has the “full confidence” of the Prime Minister.