Malcolm Turnbull and Bill Shorten during a vote that Barnaby Joyce no longer be heard during question time. Credit:Andrew Meares The internal audits by both major parties began months ago, soon after former Greens senator Scott Ludlam announced he was a dual citizen. In the Liberal Party's case, federal and state directors agreed to undertake the legal checks on all sitting members of parliament and the process has been driven by state offices, in consultation with the national office. It's understood that some, but not all states have now completed the process. Prime Minister Malcolm Turnbull's office is aware the work is underway. For Labor, the process was driven by the party's national office, working closely with Opposition Leader Bill Shorten's office, with state party offices also involved.

Greens Leader Senator Richard Di Natale wants a senate committee to audit MPs' citizenship. Credit:Dan Himbrechts A party source said that, in many cases, the process involved getting a fresh set of legal eyes to review the paperwork already produced for legal advisers during the candidate vetting process. In more complicated cases, barristers and QCs have been engaged to provide additional advice. Labor's internal process began soon after Mr Ludlam's case emerged too and it concluded after about a month. While it is not surprising the major parties would quietly run checks on MPs who could face legal hurdles, the revelation that it has been going on for months – even as Labor and the Liberals have fought off an external probe – will likely prompt calls for the findings to be publicly released. It also raises questions about whether either party has discovered another MP may be an undeclared dual citizen and kept quiet about it.

Greens Leader Richard Di Natale said the fact that behind the scenes checks were done was "a sign of a government that has lost all credibility and is no longer fit to govern". "There is now no longer any excuse for the government not to commit unequivocally to a transparent, independent audit of every single member of parliament," he said. Mr Ludlam's resignation in July eventually prompted a High Court case that found five MPs – including former deputy prime minister Barnaby Joyce – were dual nationals. Former senate president Stephen Parry then sensationally came forward and quit last week. Under the Greens' proposal, the party will attempt to set up a new senate select committee on November 13 when the Senate next sits that would co-opt citizenship experts to assess and provide advice to the committee. The committee would report back by November 27, the final sitting fortnight of the year, and make recommendations on which senators could be ineligible.

The committee would comprise three government MPs, three Labor MPs, one Green and one crossbench senator and would only examine upper house MPs. The Greens hope a similar committee could be established in the House; ideally, they want a joint committee or commission of inquiry established but recognise the government is unlikely to support this. Dr Di Natale said parliament faced a "constitutional crisis" and that "the prime minister and the opposition leader need to stop acting in their own self-interest and start acting with some integrity". The government has resisted pressure for an external audit of all MPs, arguing it would reverse the onus of proof, that the High Court should deal with citizenship matters and that an audit, as Mr Turnbull put it, would be a "witch hunt". Mr Shorten's peace offering is for "a universal disclosure to the Parliament" by all MPs but on Saturday, he failed to provide more details of how this would work even as he called for all parties to sit down and "work out a process that restores the confidence of the Australian people in the Australian Parliament".

The Greens hope their proposal will be taken up by Labor. Mr Turnbull has questioned the utility of an audit by, for example, a parliamentary committee and said MPs should simply self-report themselves. He has already dismissed Mr Shorten's call for universal disclosure as "characteristically confused".