Deputy Opposition leader Tanya Plibersek will seek to enlist Communications Minister Malcolm Turnbull as a co-sponsor to legalise gay marriage in Federal Parliament.

In a move designed to put pressure on the Coalition government over the vexed issue, Ms Plibersek says she will introduce a private member's bill to legislate for same-sex marriage following Thursday's High Court decision to strike down the ACT's same-sex marriage act.

Wedding hitch: Tanya and Shar McKinlay were married before the law was struck down. Credit:Rohan Thomson

But crucially, she says she will only introduce the bill if Prime Minister Tony Abbott allows his MPs a conscience vote on the issue.

''Mr Abbott moved to stop same-sex marriage in the ACT and the High Court has said it's for Federal Parliament to decide,'' Ms Plibersek said.