Prime Minister John Key says New Zealand will give its support to change royal succession law that bans first-born daughters from ascending the throne and another law that bans Catholics from marrying into the royal family.

The British monarch is also the Queen, or King, of New Zealand and under British law, changes to the succession rules must be approved by each country of the realm.

British Prime Minister Gordon Brown has previously said he would raise the issue at the Commonwealth Heads of Government Meeting (Chogm) in Trinidad that has just finished.

There had been widespread speculation in the British media that that would occur, but he did not raise it with either Mr Key or Australian Prime Minister Kevin Rudd, among the 15 other countries he must consult.

Mr Key said the meeting's focus on climate change might have delayed the consultation.

But he said New Zealand supported the move and he said he was questioned by British media on it.

There is believed to be cross-party support in Britain to change the law so that any first daughter of Prince William's could not be passed over for the throne by a younger brother.

However, there is no move to allow a Catholic to become the head of state because the monarch is also the head of the Church of England.

Mr Key reiterated his belief that New Zealand would become a republic but probably not while he was Prime Minister.

The Government is due to set up a constitutional view next year.

Chogm finished yesterday with leaders agreeing to admit Rwanda as a member of the Commonwealth.

Mr Key said it was a better meeting than he had been expecting - it was his first Chogm meeting - but he was surprised at how little time was spent on human rights issues. He would be willing to do more at the next Chogm in Australia.

"It was better than my expectations were. I think climate change and the close proximity to Copenhagen gave it a purpose - so it was real. It's a real issue for the members of the Commonwealth. It moved from being ceremonial to having a purpose."

Asked if he thought enough attention had been given to human rights issues, he said: "It was hardly raised so, in a word, no."

A controversial bill being proposed in Uganda that would punish homosexual acts with life imprisonment and punish "aggravated homosexuality" - having sex while HIV-positive - with execution got no mention on the floor of Chogm.

But Canadian media reported that Prime Minister Stephen Harper raised the issue privately with President Yoweri Museveni.

Mr Key said countries did not have endless opportunities to make interventions on issues and New Zealand had used its one in the executive session on Fiji.

The only criticism of Chogm he had was that leaders spent too much time debating the communique line by line - which should have been left to officials.

Mr Key returns home tomorrow night.