BT has offered to provide the infrastructure for 99% of premises in the UK to get broadband speeds of at least 10 megabits per second by 2020.
It means government-imposed rules to allow those living in remote areas to demand broadband would be unnecessary.
The universal service obligation (USO) was designed to help remote households get fast broadband more quickly.
Around 1.4 million households currently cannot get speeds above 10Mbps, according to Ofcom.
This figure is disputed by a group of MPs who say that there are a further 5.3 million who have not chosen to take up faster broadband services, some of which may also not be able to get 10Mbps speeds.
In a report published this week, they called on regulator Ofcom to more clearly distinguish between the take-up and actual availability of fast broadband.
BT's voluntary offer to provide infrastructure to almost every home could mean that the USO is no longer needed, although the government has yet to decide whether to abandon it.
The Department of Culture, Media and Sport said it would consult on BT's proposal, adding that, if the offer was accepted, it would be legally binding.
Culture secretary Karen Bradley said: "We warmly welcome BT's offer and now will look at whether this or a regulatory approach works better for homes and businesses.
"Whichever of the two approaches we go with in the end, the driving force behind our decision-making will be making sure we get the best deal for consumers."
The telecoms firm claimed that by using a range of technologies, including fibre and fixed wireless, broadband can reach 99% of the UK by 2020.
It added that it was already well on the way to offering fast services around the country, with 95% of premises able to access speeds of 24Mbps or faster by the end of 2017.
'A right to broadband'
It estimated that the rollout would cost between £450m and £600m and would largely be delivered by its spun-off network firm Openreach.
"Our latest initiative aims to ensure that all UK premises can get faster broadband, even in the hardest to reach parts of the UK," said BT chief executive Gavin Patterson.
There have been criticisms that the UK was falling behind other nations in both the availability and speed of broadband services.
The universal service obligation (USO) - which the government planned to roll out in 2020 - would have meant that everyone, regardless of where they live, would have the right to request a broadband connection, and BT would have to provide the infrastructure.
It was seen as a way to speed up broadband rollout to remote areas which for years have languished on slower net speeds because providers such as BT and Virgin Media saw no profit in offering services to areas with small populations.
Telecoms regulator Ofcom forced BT to legally separate its broadband infrastructure division Openreach in March.
The move was intended to shake up UK broadband, with the view that an independent Openreach would deliver better customer service and investment in broadband.
Since the split, Openreach has pledged to offer super-fast fibre broadband to 10 million homes by 2025, using technology known as fibre to the premises (FTTP) which it had previously said was too expensive for wide rollout.