Housing Secretary Michael Gove has written to every English council leader and all social housing providers saying they have to improve conditions.
Awaab died in Rochdale from a respiratory condition caused by exposure to mould in his family's flat.
Rochdale Boroughwide Housing's chief executive was sacked on Saturday.
Gareth Swarbrick had been in charge of the housing association since 2008.
Awaab's family first raised the issue of mould in the flat in 2017 but it had not been fixed by the time of his death in 2020.
Mr Gove sent a separate letter to housing providers saying the country needed to "raise the bar dramatically" on the quality of social housing and "empower tenants" to ensure "their voices are truly heard".
He said that housing providers should carry out assessments of damp and mould in their properties, as well as any action that may need to be taken to tackle the issue.
Awaab's inquest, which finished on Tuesday, heard that his father Faisal Abdullah - who came from Sudan to the UK in 2016 and was joined by his wife Aisha Amin a year later - reported mould in their flat to RBH in 2017 and was told to paint over it.
In June 2020, the family contacted solicitors and initiated a claim over the recurring mould issue, but policy meant any repairs would not be done until an agreement had been reached.
The inquest heard Awaab had consistently suffered from cold and respiratory issues. He died after being rushed to hospital with shortness of breath in December that year.
After the inquest finished, Mr Swarbrick, who was appointed chief executive in 2008, apologised for the organisation's response over the mould but rejected calls to quit his job, saying he had the board's "full backing".