Sajid Javid is vowing to "do right" by the people affected by the Windrush scandal as he starts his new job as home secretary.
He has rejected the controversial "hostile environment" tag attached to the government's immigration policy.
Theresa May will meet her ministers at a cabinet meeting on Tuesday for the first time since Amber Rudd quit.
Labour says the prime minister has "questions to answer" about her own time at the Home Office.
Facing questions by MPs, Mr Javid vowed to "do whatever it takes" to put right the problems faced by the Windrush generation which led to Ms Rudd's departure.
As a second generation migrant, he said he was "angry" at the treatment of those caught up in the saga.
The difficulties faced by "longstanding pillars of the community" should never have happened, he said, adding: "I thought that it could be my mum, my brother, my uncle or even me."
He told MPs: "I want to start by making a pledge, a pledge to those from the Windrush generation who have been in this country for decades and yet have struggled to navigate through the immigration system. This never should have been the case and I will do whatever it takes to put it right."
And he said he would not be using the phrase "hostile environment" to describe immigration laws introduced by Mrs May when she was home secretary.
He told MPs: "I think the terminology is incorrect, I think it's a phrase that is unhelpful and does not represent the values as a country."
Will Javid stray from May?
BBC political editor Laura Kuenssberg
Politically neat, generally welcomed by colleagues – In the recent canon of Tory events the relatively smooth landing of this appointment is an achievement in itself.
But moving Sajid Javid in, after Amber Rudd took herself out, does not end the prime minister's problems. She and Mr Javid need to move fast to cauterise the political wounds from Windrush.
He can, and did, make a more compelling and personal case in the House of Commons, showing what seems real anger about what has happened to those caught up in Windrush, and unafraid to use his own family story to display it too.
Colleagues have called him a "good operator", and "compassionate and empathetic". Many in Westminster are pointing to his own family history as the ultimate Tory dream – the boy whose dad arrived in Britain with £1 in his pocket, who through hard work ended up in the cabinet, with a portrait of Margaret Thatcher on his wall.
His appointment is also a landmark: he is the first politician from an ethnic minority to take on one of the great offices of state – the biggest jobs in cabinet.
But whatever the presentation and the political messaging, the realities of the Windrush fiasco affect real lives. It's not going to be fixed with a new face or a more sympathetic soundbite.
The Windrush generation settled legally in post-war Britain and automatically won the right to remain in the UK. However the UK government did not keep a record of many of the migrants.
Some people who do not have the paperwork to prove they are in the UK legally have been detained. Others have lost their jobs and have been denied access to free medical care.
The row has prompted calls for the government to abandon its "hostile environment" policy on illegal immigration, which Ms Rudd and Mrs May continued to defend. Mr Javid told MPs he preferred the phrase "compliant environment".
Labour MP Barry Gardiner said it would be a "mistake" if Mr Javid did not abandon the government's targets on removing illegal immigrants.
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And Labour MP and Windrush campaigner David Lammy, said promises made by the government should be urgently written into law. He criticised ministers for referring to illegal immigration in its response to the row.
Speaking in a Westminster Hall debate he said: "This not about illegal immigration. This is about British citizens, and frankly it is deeply offensive to conflate the Windrush generation with illegal immigrants to try and distract from the Windrush crisis."