The Ireland players delayed their pre-match press conference and training session after one member of the squad announced his intention to withdraw, due to his discomfort at playing against Israel.
Ireland are one of Europe's most outspoken critics of Israel's war in Gaza, and there have been numerous protests calling on the team not to fulfil the fixtures with Israel.
"What pleases us today, is that football has won," the Israel FA said in a statement at the start of its press conference.
"The separation between football and politics must be maintained, any other approach spells chaos and a dangerous slide on a slippery slope, leading to disastrous consequences for the game we all love.
"The Football Association of Ireland and the national team players did the right thing by recognising this, even if it took a bit longer than it should. Yet, it's better late than never."
The FAI, who voted in November for its board to request that UEFA suspend Israel from European competitions, passed a motion in favour of proceeding with the fixtures in July.
FAI CEO David Courell said the players would not take part in any further media obligations and would not shake hands with the Israel players before the game, in contrast to the Israeli statement.
"Flags will be raised, anthems will be played, and the players and coaches of both teams will have the opportunity to shake hands and respect each other," the Israeli statement said.
Israel are playing their home fixtures in Debrecen, and Ireland moved their home game with Israel, set for October 4, to Serbia in a match where no fans will be present.