The high court has rebuffed a challenge by Labor over Family First candidate Lucy Gichuhi’s eligibility to take the South Australian Senate vacancy, declaring her duly elected.

Labor had sought to question her eligibility at a hearing on Wednesday by raising the circumstances of her renunciation of Kenyan citizenship and whether she still enjoyed the rights of a citizen.

Gichuhi won a special recount election on Thursday after the high court ruled that Bob Day was ineligible owing to an indirect pecuniary interest in an agreement with the commonwealth.

After Day was disqualified, a Family First spokeswoman told Guardian Australia that Gichuhi had renounced her Kenyan citizenship when she became an Australian citizen “some time ago”.

Gichuhi came to Australia in 1999 and became a citizen in 2001. Kenya’s high commissioner to Australia, Isaiya Kabira, has reportedly said that Gichuhi automatically lost her Kenyan citizenship when she became an Australian citizen.

The acting shadow attorney general, Katy Gallagher, announced on Wednesday before a further high court hearing on the vacancy that Labor would “make a further submission regarding questions of eligibility”.

“In reaching this decision we have considered the advice of senior counsel. We believe there are legitimate questions to be answered.”

Gallagher said the decision was “not about Ms Gichuhi” but rather “the integrity of the Senate” as it was important that every senator’s eligibility was beyond question.

“The last thing the country needs is a rerun of the Bob Day disaster,” she said.

The high court rejected Labor’s challenge on Wednesday on the basis that there was insufficient evidence Gichuhi was ineligible and Labor had had three months to put a case together.

Gichuhi will be sworn in when parliament resumes in budget week on 9 May.

Section 44 of the constitution disqualifies any person from office who “is a subject or a citizen or entitled to the rights or privileges of a subject or a citizen of a foreign power”.

Labor’s climate change spokesman, Mark Butler, told ABC Adelaide that there were questions around whether Gichuhi had renounced her Kenyan citizenship and her “right to be a citizen of a foreign country”.

Since 2010 Kenyan citizens have become eligible for dual citizenship but Gichuhi has never applied for it.

Labor’s Anne McEwen finished just behind Day in the Senate election, making her likely to take the seat if Gichuhi is ineligible, but Butler said Labor was raising the argument on principle rather than to take the seat.

On Thursday, after the recount, Gichuhi said it had “confirmed that I am the next elected candidate to represent the state of South Australia” and she was “honoured and grateful” for the opportunity to serve.

“I am an Australian citizen and am eligible to serve. I will continue to take advice on all these matters as we move forward.”

Butler said that Gichuhi had “not been unequivocal” on the question of her eligibility.

The education minister, Simon Birmingham, told ABC Adelaide that “it needs to be sorted out” but Gichuhi and the Kenyan high commission had been “fairly clear that dual citizenship is not held and does not apply to Kenya”.

Guardian Australia contacted Gichuhi for further comment on Wednesday.