Prime Minister John Key says he is not personally opposed to gay marriage but the issue is not on the Government's agenda.
His comments follow a statement by United States President Barack Obama, who has become the first US president to affirm his support for same-sex marriage.
Mr Key said New Zealand had already changed its laws in terms of civil unions and he does not believe there is any great call for gay marriage in this country.
He said it is possible Parliament may consider a Member's Bill at some stage, but it is not on the Government's agenda.
Some MPs say gay marriage should be on Parliament's agenda. Green MP Kevin Hague says the country's reputation as a leader on these issues is at risk.
At the last election the Labour Party campaigned on a policy of legalising gay marriage, and one of the party's gay MPs, Charles Chauvel, hopes Mr Obama's comments advance the debate.
In Australia, Prime Minister Julia Gillard says her views have not changed and she remains opposed to gay marriage, the ABC reports.