The FAI has been under pressure to boycott the two matches, including a home fixture in Dublin on October 4, with several pro-Palestinian Irish politicians and football figures urging the federation to withdraw from the fixtures over Israel's conduct during the war in Gaza and the humanitarian situation in the conflict-ravaged territory.
Pro-Palestinian sentiment in Ireland is highly visible, with regular mass protests and cross-party political support for Gaza.
The Irish federation passed a motion last November requesting that UEFA immediately suspend Israel from international competition, citing breaches of the European football governing body's statutes.
"While our federation and our members have made our position clear in terms of Israel's involvement in international football, that has not been taken on board by UEFA," FAI chief executive David Courell told public broadcaster RTE on Wednesday.
"In this situation, difficult as it is, the decision presented to us only has one viable option -- which is to fulfil these games," he said.
Courell added: "We, in reality, do not have a choice for a variety of reasons."
Addressing calls to move the home game outside Ireland on security grounds amid fears protestors could disrupt the match, Courell said the game will take place in Dublin on October 4th.
Any switch to a neutral venue must be "on the basis of a formal instruction of safety and security risk. That is not the case," said Courell.
"The (Irish police) have been very clear that they are confident in their ability to deliver a safe and secure environment to facilitate the game to go ahead here."
The Israeli Football Association has said it hopes to host the Republic of Ireland in Tel Aviv for a September 27th tie, but a venue is yet to be confirmed.