Mr Murphy said ministers were "focused" on the need for reform
A cabinet minister has called for progress to be made on ending the 300-year old legal ban on Roman Catholics succeeding to the throne.
Scottish Secretary Jim Murphy, himself a Catholic, said he would like to see the 1701 Act of Settlement changed as it was clearly "discriminatory".
Catholics or those who marry a Catholic cannot become sovereign under the law.
Mr Murphy said ministers were "focused" on reforming the Act but admitted this would not be before the next election.
The Act of Settlement states that only the Protestant heirs of Sophia, granddaughter of James I, can become King or Queen.
It also gives legal precedence to male heirs in the line of succession.
The Act has been challenged over the years as being incompatible with principles enshrined in European law.
Earlier this year Jack Straw, who as Justice Secretary is responsible for constitutional matters, said the government was "ready to consider" changing the law.
Mr Murphy told The Herald newspaper that it was "wrong" to have discriminatory laws on the statute book and Mr Straw was "working hard" on plans for reform.
"I would like to see change," he said. "It is important that we make progress before the next general election.
"But the truth is it will not be changed by then."
Former home secretary John Reid said he hoped Labour would include a commitment to change the law in its next general election manifesto.
"There is now widespread recognition that this needs to be done," he said. "It is only right that any discriminatory elements against any section of our community should be removed from the British constitution."
Any move to change to the law would likely come up against opposition on both political and religious grounds.
Defending the government's record on constitutional reform recently, Mr Straw said the current Labour administration had been the most "radically reforming" government since 1945.