Hallgrimsson's side face Kosovo on Thursday in their opening Nations League game, but that fixture has taken a back seat as far as media and public interest are concerned.
Sunday's away game with Israel will take place at the neutral venue of Debrecen, Hungary, in front of a small number of Israeli supporters. The Football Association of Ireland (FAI) moved the home fixture, set for October 4, to Serbia. That game will be played behind closed doors.
At the weekend, Hallgrimsson said 'we're not playing with genocide, we're playing against genocide' and on Monday the Israeli FA responded with 'we're not playing with ignorance, hypocrisy and stupidity, we're playing against the coach who embodies them'.
Irish Prime Minister Micheal Martin defended Hallgrimsson when speaking to reporters on Tuesday, describing Israel's remarks as 'unacceptable', adding that 'Israel can't keep denying what the world knows'.
Wednesday's press conference ahead of the Kosovo game began with a question about the prime minister's comments.
"What I said at the last press meeting has taken the attention away from maybe what's most important, we are playing an important game against Kosovo," Hallgrimsson said.
"Maybe, from a leadership point of view, not clever for me to take the attention like this.
"But to answer the question, we are thankful for all the support we get. It's a tricky time for us."
Irish opposition to Israel involvement in football
Ireland has been one of Europe's most outspoken critics of Israel's war in Gaza, and FAI members voted in November for its board to request that UEFA suspend Israel from European competitions.
Israel's assault on Gaza has been described as genocide by UN experts and rights organisations, an allegation Israel rejects.
Numerous protests have taken place in Ireland in the lead-up to the fixtures and captain Dara O'Shea was asked on Wednesday if the players have any action planned for the Israel matches.
"We will come together on Friday and discuss it as a group," O'Shea said.
"I don't think we would be doing our job properly if we didn't put our focus into the game (against Kosovo).
"It's something that can't be brushed over. The decision we come to as players will be taken as one."
Irish state broadcaster RTE, which has contractual obligations to show the games, will provide stripped-back coverage.
There will be no studio presentation or punditry and commentary will be taken from the international feed. RTE has not taken advertising or sponsorship around either game.