Martin said the Israeli Football Association's remarks about Ireland manager Heimir Hallgrimsson were "unacceptable".
"I think those are unacceptable remarks. They should be withdrawn," the taoiseach told reporters in New York, where he is attending the UN General Assembly.
"Israel can't keep denying what the world knows, and what the world understands," he said.
Hallgrimsson sparked the row after saying ahead of two Nations League fixtures against Israel: "We're not playing with genocide, we're playing against genocide. We're playing against Israel, we're not playing with Israel."
The Israeli FA responded on Monday, accusing the Icelandic coach of "stupidity, ignorance and hypocrisy".
Martin said Hallgrimsson's comments reflected concerns about the scale of death and destruction in Gaza, also citing remarks by UN Secretary-General Antonio Guterres.
The dispute comes amid mounting controversy in Ireland over the fixtures, scheduled for 27 September and 4 October.
More than 160 Irish sportspeople have signed an open letter calling on the national team to boycott the matches, while protesters gathered outside the team's Dublin hotel on Monday.
Further protests are planned around the country in the run-up to the games.
The Football Association of Ireland (FAI) passed a motion last November requesting that European football governing body UEFA suspend Israel from international competition, but received no support from European football chiefs.
The FAI has said it has little choice but to fulfil the fixtures or risk sporting and financial sanctions.
Ireland's designated home match on 4 October was moved from Dublin's Aviva Stadium to Backa Topola, Serbia, following concerns over disruption and security.
The 27 September match, officially Israel's home fixture, will also be played at a neutral venue, in Debrecen, Hungary.
Israel strongly rejects allegations that its conduct in Gaza amounts to genocide.
Hamas on 7 October, 2023 led the deadliest attack ever against Israel, in which militants killed 1,221 people and dragged into Gaza some 251 hostages, 44 of them already dead, according to Israeli official figures.
Israel launched a massive retaliatory offensive that has displaced virtually the entire population at least once and has killed 73,919 people, according to the Gaza health ministry, which operates under Hamas and whose figures are generally considered reliable.
Ireland has long been a strong supporter of the Palestinian cause, with sympathy for Palestinians often linked to the country's own history of British rule.
Dublin formally recognised a Palestinian state in 2024 alongside Spain and Norway, and has repeatedly criticised Israel's conduct of the war in Gaza.