The Labor leader said cabinet ministers Barnaby Joyce and Fiona Nash should stand aside until the High Court decides their fate but is willing to discuss the matter with the prime minister.
However, he's suggested if there is a controversial vote to be had in parliament, it should wait until the High Court has made its decision.
"I think Australians want to see this government focusing on them, not these legal and political games," Mr Shorten told reporters in Melbourne on Sunday.
Attorney-General George Brandis expects High Court hearings won't occur until October.
Senator Nick Xenophon, the latest Australian politician caught up in the dual-citizenship scandal, has described it as a "festering farce" and attacked his opponents for spending hours trying to knock him off.
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Xenophon: Dual-citizenship scandal a 'festering farce'
The crossbench senator revealed he was a British overseas citizen by descent as a result of his father emigrating to Australia from a British territory.
His news came after deputy Nationals leader Senator Nash revealed on Friday she was a UK citizen by descent, the third member of the prime minister's cabinet to be affected.
Senior Nationals MP Darren Chester conceded it had been a "rotten few weeks" for his party.
"We need to be better at our vetting process when people nominate to be a candidate," he told ABC TV.
The parliament has already referred Nationals senator Matt Canavan, Greens senators Larissa Waters and Scott Ludlam, One Nation senator Malcolm Roberts, as well as Mr Joyce, the deputy prime minister and Nationals leader, to the court.
The High Court will have a directions hearing on the matter on Thursday, where the timetable of proceedings should be laid out.
"The commonwealth will be asking the court to deal with the matter urgently," Senator Brandis told Sky News.
While the court will sit in September, he thinks realistically the issue won't be heard until the first fortnight of October.
Senator Xenophon said Mr Joyce's decision not to stand down is causing disruption on the floor of the House of Representatives, where Labor spent much of the past week trying to force the government to stand the deputy prime minister aside.
"It would probably be simpler for the government if the ministers stood aside but it's really a political issue, not a legal issue," he told Sky News.
He confirmed his NXT party would still support the government on matters of confidence and supply.
Senator Brandis said government legal advice says there is no problem with Mr Joyce and Senator Nash remaining in the cabinet and making decisions.
"If there is anyone who is a threat to the integrity of the parliament at the moment (it) is Shorten because of the devious tactics he has employed," he said.
