Labor and the Coalition should abandon the Howard Government's draconian policy on certificates of non-impediment for same-sex couples and provide all Australians with equal rights to marry here and abroad, according to the Australian Greens.

In 2005 the Howard Government banned the issuing of certificates of non-impediment for same-sex couples, preventing them from being able to marry overseas. News reports suggest the Federal Attorney-General's office has restated the Government's commitment to this policy, saying it will not be repealed if Labor is re-elected.

"Given the old parties refuse to legislate for marriage equality in Australia, many same-sex couples travel overseas to marry. It's appalling that this avenue is also being closed off to them," said the Greens Spokesperson for Sexuality and Gender Identity, Senator Sarah Hanson-Young.

"It seems Labor are not content to deny Australian same-sex couples their right to marry on Australian soil, they also want to deny them that right overseas.

"Having said that, the Coalition is still committed to this policy as well - the old parties are clearly locked in the past when it comes to same-sex relationships.

"The Greens are rock solid in our commitment to marriage equality. For this, there can be no substitute. In February I introduced a bill to amend the Marriage Act, to give all Australians, regardless of sexuality, the opportunity to marry. I'll be reintroducing that Bill into the Senate after the election.

"Today, we have a Family First Senate candidate likening same-sex marriage to child abuse. These kind of offensive and homophobic comments should have no place in modern politics.

"These kind of appalling statements highlight the importance of having the Greens in the Senate. Australia desperately needs a political party that is willing to stand up against this kind of bigotry. The Greens provide that leadership."