Former Republic of Ireland manager Brian Kerr and ex-international James McClean are among those to have backed calls for a boycott of the fixtures.
The armed Palestinian group Hamas attacked Israel on 7 October 2023, killing about 1,200 people and taking 251 hostages.
In response, Israel launched a massive military offensive in Gaza, during which more than 73,000 people have been killed, according to the territory’s Hamas-run health ministry, whose figures are considered reliable by the United Nations.
Hallgrimsson relayed that nobody “can understand the pressure that has been going on these players” and said the lengthy meeting on Saturday stemmed from “a change of mind for one of the players to play the game”.
“All of the rest of the players are training today,” he confirmed.
“The balance [to play] changed with this [withdrawal] and obviously it was an ongoing discussion but we came to a conclusion and the game is going ahead.
“We will train and there will probably be more discussions tonight and probably tomorrow. It’s a unique situation and we are just trying to limit the damage.”
Republic of Ireland lost their opening Nations League fixture in Kosovo on Thursday, a match overshadowed in the build-up by the Israel games.
Asked whether the far from ideal build-up to tomorrow’s game will affect the players, the Irish boss said “we will see”.
“Nobody is comfortable but it’s about limiting the damage, both personally and for Irish football, that we need to find some solution on it,” he continued.
“There is no action we do that everyone will agree to, so we need to find a solution to limit the damage for us as a group, for Ireland as a nation and the association for football in Ireland.
“We don’t know the consequences if we don’t play the game but a lot of players share a common feeling, so there are two choices and both are tough. It’s a situation you can’t win.”