But the Attorney-General, Christian Porter, says although Ms Lamb's personal situation is unique, the MP remains a British citizen and must be referred to the High Court because of an unavoidable "legal fact".

Ms Lamb made an emotional speech in Parliament on Wednesday in which she explained why she had no relationship with her mother, which she says prevented her from gaining access to the marriage certificate requested as part of the process to renounce her British citizenship.

The Opposition Leader said the speech had been strong and courageous and, "I don’t think anyone who is fair dinkum couldn’t have been moved by what she said".

"It’s as if the summer break never happened and we are stuck in this endless loop. So what we have suggested to Malcolm Turnbull is that we have some concerns about a couple of his people, he says he has some concerns about a couple of our people, let's cut out the nonsense," Mr Shorten said.

"Let’s do a job lot [of referrals to the High Court]."

Mr Shorten said it was time to draw a line  under the citizenship fiasco, which has plagued the Parliament since last July, because Australians are angry with politicians who continue to argue about the issue.

But Mr Porter said the recent High Court decision established the "reasonable steps" test only applied when it was impossible, or next to impossible, to renounce the citizenship of another nation.

This was not the case for Ms Lamb, he said.

"As compassionate as anyone can be, and that was a very moving contribution from Susan Lamb, equally I know there was enormous distress for [former] senator Fiona Nash whose difficulty in some large part arose from the fact that she had an estranged relationship with her father," Mr Porter told Sky News.

Ms Nash was forced out of Parliament because of her British citizenship.

"The law says now what the law says and it appears to the government - and I think to most rational, independent observers - that Susan Lamb is highly likely to be in contravention of the Australian constitution, as interpreted in the recent High Court case," Mr Porter said on Thursday morning.

"The most empathetic person in the world can't change that legal fact".

He also dismissed any comparison with the cases of Energy and Environment Minister Josh Frydenberg and Liberal backbencher Jason Falinski.

"This isn't going to the High Court like Noah's Ark, two by two. Each case has to be accompanied with its individual assessment and, in each individual case, the matters are different. A referral should flow where there is a reasonably strong prima facie case that the person is in breach of the constitution," Mr Porter said.

Ms Lamb holds British citizenship through her now deceased father and began the process of renunciation shortly before the deadline for nominations at the 2016 election. Her application was rejected by the UK Home Office, which requested a marriage certificate to establish she was entitled to citizenship in the first place.

Ms Lamb said she was unable to get the document because, under Queensland law, she must get permission from her mother.

The government argues that is not the case and it is possible to obtain the document in special circumstances.