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The Labour leader has written to the PM following the announcement of the inquiry's terms of reference.
Broader questions on social housing, which campaigners say are central to the situation, will not be included.
Mr Corbyn said he was concerned the government was trying to avoid criticism for "policy failures".
At least 80 people are thought to have died in the fire in North Kensington, west London, on 14 June.
The government has announced that the inquiry, headed by Sir Martin Moore-Bick, will consider the actions of Kensington and Chelsea Council.
It will also look at the adequacy of regulations, the tower's recent refurbishment, and the response of authorities in the aftermath.
Prime Minister Theresa May said the government would meet social housing tenants to "discuss the challenges they face" and would be setting out further proposals "in due course".
In his letter to Mrs May, the Labour leader wrote: "It is, of course, a relief that the inquiry is now up and running, and that survivors are one step closer to the answers they so desperately need.
"However, I am deeply concerned by the decision to exclude the broader social and political issues raised by the fire from the terms of reference of the inquiry.
"The fire has raised profound concerns about the way that social housing is provided and managed in this country, and I - as well as many survivors - worry that, without a wider focus, the inquiry will fail to get fully to grips with the causes of the fire.
"The fear is that the priority is to avoid criticism of your party's policy failures rather than secure justice for Grenfell survivors, along with the safety of the many other people who live in social housing in this country."
Visual guide to the Grenfell Tower fire
What happened at Grenfell Tower?
The terms of reference for the public inquiry, which have been accepted in full by the prime minister, are:
Mr Corbyn also urged ministers to "reassure survivors on their immigration status" after Sir Martin suggested that a failure to address the long-term immigration status of some survivors could hinder his work.
The judge urged the government to "take all necessary steps" to encourage those living in the building illegally to come forward, adding that it could deprive the investigation of "valuable" evidence if they didn't.
The government responded to his concerns by pointing to a 12-month amnesty that would allow such individuals temporary lawful residence in the UK - but Mr Corbyn said he was "troubled" by the government's response.
"It seems clear that Sir Martin is indicating a 12 month amnesty is insufficient and that concerns remain that a number of survivors will be discouraged from participating in the inquiry as a result," he wrote.
"I therefore urge you to grant indefinite right to remain in the UK to all survivors who need it, on a discretionary basis. Failure to do so will impede their ability to contribute to the inquiry and may undermine the inquiry itself."
The inquiry has now officially begun and will hold its first hearing on 14 September, with an initial report by Easter.
Separately, The Metropolitan Police has said it would investigate "all criminal offences that may have been committed".