Ministers had faced growing pressure from Labour backbenchers about whether the security services should be treated differently from other public bodies under the new law.
The Hillsborough Law was first promised by Sir Keir Starmer when he was leader of the opposition in 2022.
However, the bill’s progress through Parliament stalled earlier this year over disagreements between the government and campaigners about how the new legal duty of candour should apply to spies.
The previous proposal was that the chiefs of the intelligence services would be able to veto officers from giving evidence that could potentially risk breaching national security.
Under the government’s new plans, the security services would instead have to make a specific court application if they wanted an exemption from the law.
The government said it was working with the Hillsborough families to “get this bill right”.