The Queen has said women should have a greater role in society, as she opened a Commonwealth summit which will discuss the law on royal succession.
Countries with the Queen as monarch have to decide whether they want sons and daughters of any future UK monarch to have equal right to the throne.
The Queen's speech in Perth, Australia, did not mention the issue but did highlight equality as a key issue.
Prime Minister David Cameron said he would be backing the change.
Under the current succession laws, dating back more than 300 years, the heir to the throne is the first-born son of the monarch. Only when there are no sons, as in the case of the Queen's father George VI, does the crown pass to the eldest daughter.
Arriving in Perth, the prime minister said the marriage of Prince William this year meant the issue could not be deferred any longer.
"I think the time has come to change the rules so that if the royal couple have a girl rather than a boy then that little girl would be our queen," he said.
In her comments to the summit on female equality, the Queen said: "It encourages us to find ways to show girls and women to play their full part."
The BBC's royal correspondent, Nicholas Witchell, said this was a hint that the Queen herself backed the change.
The laws of succession are not a matter for the 54-nation Commonwealth as a whole, only for the 16 countries which have the Queen as their head of state.
The royal author Robert Hardman says there have been 11 attempts in recent years by individual MPs and peers to change the law.
Lord Archer tried with a private member's bill in 1997. He says the Queen indicated then that she backed change.
"Thirteen years ago when I put the bill to the House of Lords, she `let it be known` that she did not disapprove of the idea," he said.
"I just thought it would be farcical that if William and Kate have three girls in a row and then a boy, the boy leapfrogs over all three girls and becomes king."
The summit - which represents some 2bn people around the globe - will also discuss economic growth, climate change and human rights.
Most Commonwealth leaders are attending the two-day gathering.
However, Indian Prime Minister Manmohan Singh has pulled out without giving a reason, according to the AFP news agency.
Thousands of police have been deployed on the streets around the Perth Convention and Exhibition Centre ahead of the summit in the western Australian city.
The Commonwealth Heads of Government Meetings (CHOGM) are held every two years, and present an opportunity for developed and developing nations with current or former ties to Britain to discuss a range of issues.
But already other a number of divisive subjects have come up at this year's gathering, the BBC's Duncan Kennedy in Perth reports.
They include the human rights record of Sri Lanka - which is due to host the next summit - and moves to get rid of laws in some member states which discriminate against gay men and lesbians, our correspondent says.
And the leaders will discuss a 200-page report on reforms to the Commonwealth itself, including the appointment of a commissioner for human rights.
The report says the organisation is in danger of becoming irrelevant, unless it becomes more visible on the world stage and more pro-active in global affairs.