Immigration minister Brandon Lewis said the government “believed it is right” to give survivors greater certainty.
Meanwhile, the chancellor has said the government will not “automatically” fund fire safety measures for councils.
In a statement, Mr Lewis wrote: “Our initial response to this terrible tragedy was rightly focused on survivors’ immediate needs in the aftermath of the fire and ensuring they could access the services they need to start to rebuild their lives.
“However, since the Grenfell Tower immigration policy was announced, we have been planning for the future of those residents affected by these unprecedented events”.
He added that the granting of permanent residency would depend on the completion of security and financial checks. Anyone wishing to apply for permanent residency under the proposal must come forward by 30 November.
However, he insisted that all “safety-critical” changes would be made.
The chancellor said the government would act when it was certain that a council “genuinely does not have any available resource”.
The measures could include the removal of flammable cladding and retrofitting sprinkler systems in council-owned tower blocks.
Councils said many of the changes had been recommended by local fire services.
On 16 June, two days after the Grenfell fire which claimed at least 60 lives, Communities and Local Government Secretary Sajid Javid pledged that the government would “do whatever it takes” to improve safety in tower blocks.
Yet several councils have already complained that money has not been forthcoming.
The leader of the Labour opposition group on Westminster City Council, Adam Hug, said the local authority had struggled to secure funding from Mr Javid’s department to pay for the removal of cladding and the installation of sprinklers.
“Ultimately these are things that the London Fire Brigade says have to be done and ultimately the cost is having to be borne by the housing revenue account, which is tenants’ rents and service charge fees,” Mr Hug said.