But the court found Mr. Joyce was a New Zealander by descent at the time of his nomination past year.
He said he had no reason to believe he was a citizen of any other country.
"We have the support of a majority of members", Turnbull said.
"The decision of the court today is clearly not the outcome we were hoping for but the business of government goes on", Prime Minister Malcolm Turnbull said this afternoon. A no-confidence vote would require all independent and crossbench lawmakers to turn against the government.
Australia's constitution prohibits dual citizens from being elected.
It tumbled to a 0.8 per cent loss after the court disqualified Deputy Prime Minister Barnaby Joyce, forcing a by-election, but it bounced to close down 13.1 points, or 0.22 per cent, at 5903.2.
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Most of the disqualified MPs were considered born to Australian parents overseas, or had been born in Australia to a foreign parent.
Deputy Nationals leader Senator Fiona Nash, plus senators Malcolm Roberts, Scott Ludlam and Larissa Waters were also ruled ineligible as the citizenship issue reached its end. Because of the way members of the upper house are chosen, replacing them will not require by-elections.
In July, two senators in the Australian Greens stepped down from their positions after discovering they were a New Zealand and a Canadian citizen respectively.
The High Court of Australia decision means three of the politicians, including Mr Joyce, are disqualified from office.
Another government minister Matt Canavan, who the court heard might have inherited Italian citizenship from his Australian-born mother through his Italian grandparents, was allowed to stay in Parliament.
The fate of Deputy Prime Minister Barnaby Joyce is most crucial to the government in an unprecedented political crisis.
Joyce told lawmakers in August he had discovered he was a New Zealand citizen, throwing his position in parliament into jeopardy.