The federal Labor caucus will allow its deputy leader to introduce a private bill to parliament that aims to legalise same-sex marriage.

But the bill’s introduction will be subject to Liberal MPs being allowed a conscience vote.

“Marriage equality’s time has well and truly come,” Tanya Plibersek said in a statement after a meeting of the caucus in Canberra on Tuesday.

She called on the prime minister to allow his MPs and senators a free vote on the bill.

“Liberal MPs pride themselves on being able to cross the floor on issues – Tony Abbott needs to confirm that includes marriage equality.”

The text of the bill is similar to legislation introduced by Labor MP Stephen Jones which parliament voted down in 2012.

Ideally, Ms Plibersek would like a Liberal MP to co-sponsor the bill.