If the Republic of Ireland team plays Israel, it "will be a stain on Irish soccer", the Dáil has heard.
Ireland was drawn against Kosovo, Israel and Austria in Group B3 in the upcoming UEFA Nations League.
The two games between Ireland and Israel are to take place next September and October.
The away fixture will take place on 27 September, while the return leg in Dublin is scheduled for 4 October.
The FAI said it intends to fulfil the fixtures.
Last year, the FAI voted to submit a motion to UEFA to ban Israel from European competitions.
Solidarity-People Before Profit TD Ruth Coppinger in the Dáil called for a popular boycott of the upcoming game, saying this could lead to "a domino effect".
"It's an inconsequential tournament - it's not the World Cup play-offs or anything like that," she said during Leaders' Questions.
Tánaiste Simon Harris responded that her comment was "a bit sneery" as the tournament may not be inconsequential to the players.
Ms Coppinger asked if he agreed that "there is a time to take a stand in sport, and that the Ireland versus Israel soccer fixture is exactly that time".
She claimed that racism is normalised in Israeli sport.
"We should not be complicit in normalising a team that's integrally connected to a genocide, to racism against Palestinians and to the oppression of the Palestinian people," she said.
Ms Coppinger said that "Ireland has been in this situation before" in relation to apartheid, and made a positive reference to former taoiseach Charles Haughey's handling of the issue.
Mr Harris rejected Ms Coppinger's assertions and said Ireland continues "to work for a two-state solution".
He said when it comes to sport a logical assessment is needed, and in this case the FAI made a determination, and UEFA then "decided not to take that view on board".
"The tournament is going ahead," he added, warning that if Ireland pulls out it could harm Irish soccer.
Mr Harris also criticised the targeting of individual players in an attempt to pressure them.
