An MP has welcomed the Home Secretary's "rhetoric" and joked about her possibly joining his party.
Danny Kruger, the East Wiltshire MP, recognised Ms Mahmood's position but said they would not stop "the lawfare".
Mr Kruger defected from the Conservatives to Reform UK earlier this year.
He warned that these measures would not stop the legal tactics used by failed asylum seekers to delay and block their removal.
On Monday, Ms Mahmood announced several measures to "tackle the pull factors that draw people into this country".
These include stopping benefits for refugees who "are able to work but choose not to".
She also plans to change the UK's interpretation of Article Eight of the European Convention on Human Rights (ECHR)–the right to respect for private and family life–so that "family" means only "parents and their children".
Asylum seekers will only be able to use this right to lodge claims if they are already in the UK.
Mr Kruger told the Commons: "I welcome the rhetoric that the Home Secretary has announced.
"In fact, I recognise the rhetoric of the Home Secretary today–we have our plan for restoring justice, she's announced a plan to restore order and control.
"But before she puts in her application to join Reform UK, and I'd very much welcome her doing so, can I draw out the difference between our parties?
"Unlike the Government, we don't propose to give illegal immigrants the right to stay here for two-and-a-half years after arriving, we don't propose to give them the right to study and work here, we don't propose to allow them to bring their families here, and crucially, we're not going to contort our law to fit in with the ECHR."
In response to his invitation to join Reform UK, Ms Mahmood said: "Over my dead body."
Conservative leader Kemi Badenoch described some of the measures as "baby steps, but positive".
Sir Edward Leigh, the Gainsborough MP, also said Ms Mahmood "clearly has strong Conservative instincts" and suggested she should be open to ideas like the now-cancelled Rwanda scheme, to remove asylum seekers to Africa if they crossed into the UK without permission.
Ms Mahmood replied: "On Rwanda, no."
However, Ms Mahmood faced criticism for her announcement from Liberal Democrats home affairs spokesman Max Wilkinson.
He said: "What is not helpful is the Home Secretary claiming that the country is being torn apart by immigration."
Ms Mahmood said in her response: "I wish I had the privilege of walking around this country and not seeing the division that the issue of migration and asylum system is creating across this country.
"Unlike him, unfortunately, I am the one that is regularly called a f****** Paki and told to go back home.
"It is I who knows, through my personal experience and that of my constituents, just how divisive the issue of asylum has become in our country."
Former Labour leader Jeremy Corbyn accused Ms Mahmood of "trying to appease the most ghastly right-wing racist forces all across Europe in undermining and walking away from the ECHR, a convention created by the post-war Labour government".
Many asylum seekers have arrived from Afghanistan, which the UK "helped to make into a war-torn country", the Your Party co-founder added.
He asked: "Does she not recognise history is going to be a harsh judge on this Government for undermining the whole global humanitarian principles behind the ECHR and the Universal Declaration of Human Rights?"
Claimants from Afghanistan have had access to "bespoke schemes", Ms Mahmood replied.
The Cabinet minister said she wanted to "incentivise people coming on safe and legal routes instead" of by crossing the English Channel on small boats.
Ms Mahmood also said she was "sorry to find that the Reform party is living rent-free in so many people’s heads" but that it was "nowhere near" hers, after Plaid Cymru Westminster leader Liz Saville Roberts told MPs "imitating Reform doesn’t create unity, doesn’t win trust".
