Mahmood is expected to double down on her approach in a speech next week.
She will seek to make a “Labour case” for “firm and fair” Danish-style immigration policies, which are aimed at reducing incentives for people to enter the UK illegally.
Left-wing Labour MPs have called for a change of approach.
Richard Burgon – of the Socialist Campaign Group – told the BBC it was time to “ditch the approach of aping Reform and kicking the left which has alienated so many people who have voted Labour previously”.
Imran Hussain, from the Refugee Council, a charity, was sceptical about proceeding with new asylum and immigration rules.
He said that “the big lesson of recent years was that tough talking” did not lead to “smart action” and the government should instead focus on the “basics” – swifter asylum decisions, swifter appeals and help for refugees to integrate.
Reform UK’s home affairs spokesman Zia Yusuf said Mahmood was “all talk and no action,” and the government could not fix the immigration system while it was “chained” to the European Convention on Human Rights (EHCR).
He said a Reform government would leave the ECHR immediately and “completely abolish indefinite leave to remain”, as well as imposing visa bans on countries refusing returns and “criminalise aiding illegal entry, regardless of intent”.