Irish Premier Leo Varadkar said he will raise the outcome of Emma DeSouza's case with Boris Johnson this week.
In 2017, the Northern Ireland woman won a case against the Home Office after it deemed she was British when her US-born husband applied for a residence card.
The Good Friday Agreement allows people to identify as British, Irish or both but on Monday an immigration tribunal upheld an appeal of the case, brought by the Home Office.
Sinn Fein leader Mary Lou McDonald called on Mr Varadkar to step up to defend the Good Friday Agreement in light of the ruling.
"I invite you to insist that the Prime Minister Boris Johnson moves at speed to introduce the required legislation through Westminster to ensure that our Irish citizens living in Ireland are recognised and respected as Irish," said Ms McDonald.
"You now need to step up and defend Emma, defend her rights and the rights of all Irish citizens," she said.
Mr Varadkar said the Irish Government will continue to uphold the Good Friday Agreement and respect the fact that people in Northern Ireland have the right to be British or Irish or both.
"This judgment appears to make a distinction between identifying as British or Irish, as opposed to being a citizen.
"And that is a misreading and our view of the Good Friday Agreement, so we will continue to seek an outcome of that review with the Secretary of State, and I will raise it with the Prime Minister," he told the Dail on Tuesday.
"I raised it in the past from Prime Minister May, and will do so again on Thursday or Friday with Prime Minister Johnson.
"Last February when it was raised with Prime Minister May, she acknowledged the serious and real concerns in this area pledged to review the issues around citizenship urgently to deliver a long-term solution consistent with the letter and spirit of the Good Friday Agreement," he said.
Mr Varadkar said the Irish Government is "actively seeking" an outcome of the review and would also be raising it with the Northern Ireland Secretary of State Julian Smith.
In response to Ms McDonald, Mr Varadkar said he would not be making demands of the British Government in relation to Ms DeSouza's case.
"I know you're suggesting a stronger approach that I insist and demand. If that approach was effective, you would be in government in Northern Ireland. That's not the approach that actually works in the real world.
"You raise things with people in a logical respectful and consistent way, insisting and demanding is how you get nowhere. And that's why you got nowhere in the North," he said.