MELBOURNE (Reuters) - Thousands of Australians marched at same-sex marriage rallies across the country on Saturday calling on whichever party wins a July 2 national election to quickly introduce same-sex marriage laws.

Gay rights activists hold a rainbow flag during a rally to support same-sex marriage in central Sydney in this file photo from August 11, 2012 . REUTERS/Daniel Munoz

Conservative Australian Prime Minister Malcolm Turnbull supports same-sex marriage and has pledged a public vote on the issue before the end of 2016.

The Labor opposition will skip a public vote and introduce a bill to parliament within 100 days if it wins the election.

Opinion polls say Turnbull’s conservative coalition and Labor are neck-and-neck ahead of the election.

Protesters in Sydney, Melbourne, Brisbane and Perth marched carrying rainbow flags and signs which read “Equality now”.

Some dressed up in costumes of former primer minister Tony Abbott, an opponent of same-sex marriage, who Turnbull ousted in a party room coup last September.

Openly-gay Labor candidate Pat O’Neill, who marched in Brisbane, said the election will give the gay community a “voice at the ballot box”, reported Australian Associated Press (AAP).

Greens Senator Larissa Waters told the crowd a public vote was a waste of time. “It’s not going to be binding on their (government) members - what a joke,” said Waters, reported AAP.

Australia has been criticized by international human rights groups over its slowness to act on same-sex marriage. Several countries, including Canada, the United Kingdom, United States, France, New Zealand, Ireland and South Africa, have already amended their marriage laws to recognize same-sex unions.

Turnbull, considered a moderate, brushed off criticism from conservatives to become the first sitting prime minister to attend Sydney’s annual gay Mardi Gras parade in March.

Australia has seen a revolving door of political leadership in recent years. If Turnbull loses on July 2, the change in prime minister would be the fifth since 2010.