The regulator has proposed new legislation that will see the telecoms giant required to fix faults within two working days and install lines for new customers in 12 working days.
These targets are to be met at least 80% of the time and will be gradually introduced over a three-year period.
Besides this, BT will be expected to publish figures relating to how well its engineers are performing and Ofcom will have the ability to impose fines if services are not delivered on the new timescales.
Before the regulatory proposals can become mandatory, they must be reviewed by the European Commission, to which the organisation has already submitted its new guidelines.
Ofcom claims the new potential rules are intended to ensure better service for telephone and broadband customers in the future.
The regulator has also revealed that it intends to cut start-up fees so new customers can get Internet access and a telephone line at a cheaper price.
It explains this is because companies must currently pay £50 switching fee to Openreach when a customer wants to swap providers and this fee is often passed to the consumer.
Ofcom explained that is intending to get this fee lowered to £11 instead, allowing superfast broadband providers to offer lower start-up fees.
Should the new measures be accepted, the regulatory claims that targets set will be adjusted slightly to account for external factors such as extreme weather that may prevent Openreach from hitting its targets.