Giving male heirs priority in the line to the throne is “outdated and wrong" David Cameron said, as he arrived in Australia for a summit of Commonwealth countries, which is expected to endorse reform.
The Prime Minister said the marriage of the Duke and Duchess of Cambridge this year was the ideal spur to change the 400-year-old rule so that if their first child was a girl she could become queen.
Downing Street is also confident of securing support from the 15 other countries where the Queen is head of state for scrapping the bar to the monarchy of anyone who marries a Catholic.
"These rules are outdated and need to change," Mr Cameron said before the opening of the bi-annual Commonwealth Heads of Government Meeting (CHOGM) in Perth, which the Queen is attending.
"The idea that a younger son should become monarch instead of an elder daughter simply because he is a man just isn't acceptable any more. Nor does it make any sense that a potential monarch can marry someone of any faith other than Catholic.
"The thinking behind these rules is wrong. That's why people have been talking about changing them for some time.
"We need to get on and do it."
Any change would require the agreement of all 16 Commonwealth "realms" - the UK, Australia, New Zealand, Canada, Jamaica, Antigua and Barbuda, the Bahamas, Barbados, Grenada, Belize, St Christopher and Nevis, St Lucia, the Solomon Islands, Tuvalu, St Vincent and the Grenadines and Papua New Guinea.
It will involve amendments to some of Britain's key constitutional documents, such as the Bill of Rights and Coronation Oath Act of 1688, the 1701 Act of Settlement and the 1706 Act of Union with Scotland, as well as changes to legislation in some other realms.
Mr Cameron wrote to them all ahead of the summit asking them to make preparations and agreement is expected to be reached.