Tony Abbott believes the ongoing dual citizenship "circus" must end but has stopped short of backing an audit of all members of federal parliament.
Other conservatives within the coalition government including Eric Abetz, Kevin Andrews and Andrew Broad are pushing for an audit, but Mr Abbott says it's up to Prime Minister Malcolm Turnbull to decide on a resolution.
"Until this matter is resolved I think that it's going to be an ongoing circus and governments and countries can't afford to have an ongoing circus of this type," the former prime minister told Ray Hadley on 2GB radio on Monday.
"Every day it's someone else - it was Josh (Frydenberg) last week, now it's Alex Hawke, it'll probably be someone else tomorrow - that's why this matter does need to be resolved."
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Frydenberg questions are latest twist in citizenship saga
The ongoing citizenship saga is driving a deep wedge through the Turnbull government, with Nationals MPs lining up behind one of their own to fill the plum post of Senate president.
The Senate presidency has always gone to a Liberal when the coalition is in power.
But Nationals senator Matt Canavan, who survived a close shave over his own citizenship, is backing John "Wacka" Williams for the $355,000-a-year job vacated by Liberal Stephen Parry.
"Senator Williams is a fine senator and of course would make an excellent candidate for the presidency," the cabinet minister told ABC radio on Monday, echoing the sentiments of high profile Nationals colleagues.
"I see no reason why a Nationals Party member or senator should not be considered for the presidency."
Senator Canavan also sympathised with Senator Williams lashing out at Liberal "cowards" and "bastards" who spent weeks anonymously criticising the Nationals over Barnaby Joyce and Fiona Nash's citizenship woes.
Nationals Senator John Williams is being suggested for the role of president of the upper house. Source: AAP
"It is cowardly and unfortunately it does cause a reaction from time to time. I can understand Senator Williams' frustration," Senator Canavan said.
The Australian Electoral Commission on Monday will conduct special recounts of Senate votes in three states to replace four dual-citizen senators the High Court booted out of parliament.
Nationals deputy leader Fiona Nash (NSW), former Greens senators Scott Ludlam (WA) and Larissa Waters (Qld) and One Nation senator Malcolm Roberts (Qld) were all ruled ineligible.
Former Democrats senator Andrew Bartlett is likely to replace Ms Waters while 23-year-old student Jordon Steele-John is expected to take Mr Ludlam's seat.
It's likely Mr Roberts will be replaced by the next in line on the One Nation ticket, Fraser Anning.
Ms Nash's Senate seat will likely go to the next person on the NSW coalition ticket, Liberal Hollie Hughes, which could further upset the Nationals.
The Turnbull government continues to resist calls for a citizenship audit, despite momentum growing among backbenchers, independents and minor parties.
"I think we just have to get a grip on this," Treasurer Scott Morrison told ABC radio.
"We've got a very big agenda of things still to be doing this year and I don't think the public would want to see us distracted by a genealogy commission."
Deputy Prime Minister Barnaby Joyce was also disqualified from parliament, but has a chance to win back his lower house New England NSW seat at a by-election on December 2.
