Ancient laws banning Catholics from the British throne should be changed, David Cameron has said.
"It's right to discuss both sets of changes. Both changes should be made, in principle," he said.
However, Mr Cameron warned that any change will take time because it would have to be agreed by all 15 Commonwealth states where the Queen is head of state.
"It will take time. We ought to have proper discussions with other countries. She is their queen after all. "
Under the 1701 Act of Settlement and it associated laws, a Roman Catholic cannot legally take the throne. Nor can someone married to a Catholic.
On Saturday The Telegraph revealed how Nick Clegg, the Deputy Prime Minister, is actively pursuing the plan to scrap the principle of male primogeniture from the monarchy in order to grant any future princesses born to the couple the same rights as male children.
Under current arrangements, the Prince’s first born son would be next in line to the throne, even if he had an older sister.
Mr Clegg, who is responsible for constitutional reform within the Government, is seeking to change this so that in future the line of succession is determined without regard to sex.
He has already raised the matter at the Privy Council, and is understood to have obtained the Queen’s consent to the move if this proves to be the will of the people.
As the British monarch also acts as the head of state of a number of Commonwealth nations, any change to the line of succession would require legislation in 16 separate countries.
An attempt by the Labour peer Lord Dubs to alter the line of succession with a private members bill in 2005 was seen off by Tony Blair’s government.
At the time, Lord Falconer, the then lord chancellor, said that the move was not a priority, because Princes William and Harry were young and unmarried.
However, following the Royal Wedding later this month, Mr Clegg is said to believe that the matter has become more pressing, with the possibility of a baby princess arriving within a year.
A spokesman for the Deputy Prime Minister said: “The Government is aware that this is an issue but it is a complex and difficult matter that requires careful and thoughtful consideration.
“Nick, like many people, is very sympathetic to the view that the current rules are discriminatory and should change.
“However, it is not as simple as it seems. There is a lot of work to do and the Government has already started discussions with those Commonwealth countries who would be directly affected.”
Moves were begun by Gordon Brown under the last government to secure the agreement of the Commonwealth to the move to allow Catholics to inherit the throne.
If the rule of male primogeniture was scrapped, and if Prince William and Kate had yet to bear children, the Princess Royal would be promoted to fourth in line to the throne, after the Prince of Wales, the Prince and Prince Harry.
Her son Peter Phillips would move from 11th to fifth in line, followed by his daughter, Savannah, who would move from 12th to sixth, and Zara Phillips, who would go from 13th to seventh.
The Duke would move from fourth to eighth in line to the throne, to be followed by Princess Beatrice and Princess Eugenie.