Senator Canavan has conceded he has been an Italian citizen since he was 2 - when he previously blamed a 2006 application by his mother - while Senator Roberts appeared to admit that he had not filled in his British citizenship renunciation documents until after he was elected.

The Turnbull government now faces months of political uncertainty as the High Court, sitting as the Court of Disputed Returns, knocked back a request by Attorney-General George Brandis for a September hearing into the validity of the MPs.

The case will be heard in Canberra over three days from October 10.

The court will consider if foreign citizenship meant Barnaby Joyce, Senator Canavan, Senator Roberts, Scott Ludlam and Larissa Waters were not validly elected, while both Nationals senator Fiona Nash and key Senate powerbroker Nick Xenophon will have their cases referred when Parliament resumes on September 4.

While the government is confident that Mr Joyce - the only lower house MP involved in the case - will be found to have been validly elected, Labor will capitalise on the uncertainty - and the fact that he and Senator Nash have not resigned from cabinet as Senator Canavan did - to attack the government.

Constitutional law professor George Williams told Fairfax Media, given the court was examining seven cases simultaneously, it could be well after October before the matter was put to bed.

"We need a judgement from them, and their reasoning ... it's unlikely we will get a result on the day. It could take some weeks after the [October] hearing to get a result," he said.

High Court Chief Justice Susan Kiefel said during the hearing the court accepted the cases had "a high degree of importance" and were matters of urgency – but there was "urgency and urgency".

Robert Newlinds, SC, acting for Senator Roberts, successfully argued for more time and suggested there was confusion over when the British authorities accepted his renunciation of dual-citizenship, something the senator has said would be made clear in the High Court hearings.

Mr Newlinds said his client did not concede he was a citizen of any other country but Australia, but told the court the case would centre around the dates he took steps to clarify his citizenship with British authorities.

Senator Roberts had emailed the British Home Office before the election to renounce his citizenship, but did not hear back, and emailed again to "renounce" his citizenship.

Senator Roberts was sent a form by the Home Office after the election, and sometime later, the British authorities accepted his renunciation.

Mr Newlinds said it remained unclear whether the Home Office "were accepting the renunciation by the form, or the earlier email".

Senator Roberts had previously said he had all the necessary documentation to prove he was eligible to stand at the last election.

Under section 44, part (i) of the Australian constitution, a person is disqualified from standing for Parliament if they are "under any acknowledgment of allegiance, obedience, or adherence to a foreign power, or is a subject or a citizen or entitled to the rights or privileges of a subject or a citizen of a foreign power".

The directions hearing also revealed a major change in Senator Canavan's argument, with lawyers for the former cabinet minister arguing he had been an an Italian citizen by descent since he was two, because of a change in Italian law in 1983. His lawyers argued that citizenship by descent rather than birth should be ignored for the purposes of section 44(i) of the constitution.

Barrister David Bennett, QC, acting for Senator Canavan, said Australian Bureau of Statistics data would reveal "a very high proportion of Australians, possibly in the order of 50 per cent" would be disqualified from sitting in Federal Parliament because of citizenship by descent and this reading of section 44 was "ridiculous" and should be excluded.

This marked a major shift from the senator's previous argument that his mother had signed him up as a citizen in 2006 without his knowledge.

After the hearing, Senator Brandis argued the court had accepted the spirit of what the government was attempting to do in accelerating the matter.

Prime Minister Malcolm Turnbull said again he was "very, very confident that our members who have been caught up in this will be held by the court to be eligible to sit in the Parliament and therefore eligible to be ministers.".

However, If Mr Joyce is found to have not been validly elected, a byelection with a minimum campaign period of 33 days will have to be called and held late in 2017 or even early in 2018.

Solicitor-General Stephen Donaghue, QC, for Senator Brandis, signalled he would argue Mr Joyce and Senator Canavan were not disqualified from Parliament, and former Senator Waters "may well be in the same situation", but there was no dispute that former senator Ludlam was disqualified and there would be a contest over Senator Roberts' ability to remain in Parliament.

Dr Donaghue said there was a "clear demarcation line" between politicians such as Mr Joyce, who had not known they were foreign citizens, and those such as Senator Roberts who had been aware of their foreign citizenship. Those in the former category were not caught by s44(i), he said.

The submissions from the Greens senators accepted they were dual citizens at the time of their nomination for Parliament and that their Senate seats should be filled by a recount.

with Emily Woods