Former Greens senators Larissa Waters and Scott Ludlam are unlikely to be pursued by the Federal Government to repay their close to $200,000-a-year salaries, after the Government waived the debt for other disqualified senators.

Greens leader Richard Di Natale urged the Government not to chase his former colleagues, after they were forced to quit Federal Parliament upon discovering they held dual citizenship.

The Constitution bans dual citizens from being elected, unless they have taken all reasonable steps to renounce their foreign allegiance.

Prime Minister Malcolm Turnbull sledged the minor party for being "incredibly sloppy" in losing two senators for Constitutional breaches.

Because the two former senators were ineligible to hold office, it was normal practice for the Department of Finance to request they pay back their base parliamentary salaries of $199,040 per year.

However, the Federal Government has previously offered to waive that debt for two other senators recently disqualified from office — Bob Day and Rod Culleton.

"[Mr Ludlam and Ms Waters] have done their job, they've represented their states, they've continued to legislate in the parliament," Senator Di Natale told ABC RN.

"I would be shocked if they were to conclude that Senator Ludlam and Senator Waters should be treated differently to Senator Day."

If the department does request their debt be repaid, the former senators will also be able to request the Federal Government waive the debt.

Sorry, this video has expired Resignations raise questions over Greens leadership and legislation

Greens debacle shows 'extraordinary negligence'

Senator Di Natale has ordered a review of his party's procedures to ensure such a bungle cannot happen again, but Mr Turnbull argued the damage to the Greens' reputation has already been done.

"It is pretty amazing, isn't it, that you have had two out of nine Greens Senators didn't realise they were citizens of another country," he told Channel Nine.

"It shows incredible sloppiness on their part.

"You know, when you nominate for Parliament, there is actually a question - you have got to address that Section 44 question and you've got to tick the box and confirm that you are not a citizen of another country.

"It is extraordinary negligence on their part."

There are another 23 members and senators who were born overseas, and all told the ABC they comply with the Constitution's citizenship requirements.

Labor leader Bill Shorten argued he was confident his party had rigorous checks and balances for its candidates, and seemingly agreed with Mr Turnbull's sentiments.

"I think Australians will say 'what is going on with the Green political party? Are they ready to be serious political operators? Are they up for the job?'

"And so I think that this sort of inadvertently damages people's confidence.

"Do they know what they're doing? Full stop."