Taoiseach Leo Varadkar has said that Israel has a right to defend itself, but that current solidarity could "fall apart" if it goes "too far in terms of its actions in Gaza".
Mr Varadkar said that Ireland is calling for restraint, and said that any response from Israel to the Hamas attacks must be proportionate.
Speaking on RTÉ's Nine News, he said that the Government was particularly concerned for the welfare of Irish-Israeli citizen Kim Damti, who has been unaccounted for since attending a music festival targeted by Hamas on Saturday morning.
He said he did not believe anyone's heart "could not go out to the family".
Mr Varadkar added that he was horrified at the targeting of civilians in Israel and Gaza, in particular the killing of women and children and the taking of hostages.
He said: "One thing Hamas has done is attack not just the people from Israel, but citizens from many other countries as well.
"From Ireland's point of view, we are saying to Israel that 'yes you have a right to defend yourself, you are surrounded by enemies who want to end your existence, but any response must be proportionate'.
"There’s a lot solidarity internationally for Israel at the moment – I believe that will fall apart if Israel goes too far in terms of its actions in Gaza.
"And there’s a risk then of violence flaring up in the West Bank and Lebanon and other places, so we’re very much calling for restraint."
Earlier, Tánaiste and Minster for Foreign Affairs Micheál Martin said that Ireland will be "very clear" that EU humanitarian aid must continue to reach Palestinians.
Speaking to RTÉ News, he said that he had been through the first stage of a special meeting with EU foreign ministers, and that "there is horror in respect of the scale of the atrocities committed against Israel and Israeli civilians following the attacks by Hamas".
He said there is concern about the evolving situation on the ground in Gaza in respect of Palestinians, families and children.
Mr Martin said: "The move by Israel to engage with Hamas and to deal with Hamas, that obviously will have consequences on the humanitarian side, and our contribution later will be very clear that humanitarian aid from the European Union has to continue to reach Palestinians in the area if education, in the area of health, and in the area of food provision."
He added that there is "real concern about the capacity of this situation to escalate wider across the region," and every effort should be made to ensure this does not happen.
Following the meeting tonight, he said he "reiterated our firm condemnation of Hamas' repugnant attacks, underlined the importance of principled and clear action by the EU, and emphasised the importance of moving towards de-escalation, and the need to protect civilians in line with international law".
Mr Martin added: "I was clear that continued development and humanitarian support to the Palestinian people is essential.
"I underlined that the review of by the European Commission's development cooperation funding needs to take place as rapidly as possible and in close coordination with member states.
"I welcomed the confirmation that EU humanitarian aid to Palestinians will continue uninterrupted, for as long as needed."
Tonight, people gathered at the Israeli embassy in Dublin to hold vigil for those who died in the attacks.
People held photos of those who were killed, and left candles and flowers outside the gates.
Another demonstration was held in support of the people of Gaza last night.
The Department of Foreign Affairs said it is closely monitoring the situation in the Middle Eastern region.
It said that the ongoing attacks "pose a significant security risk" and that citizens already in Gaza or the West Bank should remain in place until advice on crossing points is issued.
It asked that Irish citizens in Israel or occupied areas of Palestine register with the embassy in Tel Aviv.
