She's the South Australian senator who keeps her private life private.

But as debate about same-sex marriage in Australia heats up, senator Penny Wong delivered a blunt message for the government's Senate leader Eric Abetz: "Memo to Eric: we've already got children, all you are doing is saying the parents can't be married."

Penny Wong and partner Sophie Allouache and their daughter Alexandra in 2011. Their second daughter, Hannah, was born earlier this year. Credit:David Mariuz

A clearly angry Senator Wong, who rarely discusses her life with her two young daughters and partner Sophie Allouache, took aim at Coalition MPs who have argued against same-sex marriage on the basis that children should be raised in a marriage between a man and a woman.

"I find it sad that senior politicians in this country seem to want to tell my children and children of other same-sex couples that somehow they are not normal," Senator Wong told ABC radio on Monday.