The Tánaiste summoned the Israeli ambassador to Ireland to express 'Ireland's shock and dismay' at the violence
Fresh protests are expected in Gaza, a day after Israeli forces killed more than 50 Palestinians and left thousands of others injured during a day of demonstrations.
The Palestinian Health Ministry has confirmed that 58 Palestinians were killed on Monday, including six children.
Laila al-Ghandour, an eight-month-old baby, was declared dead just after midnight due to teargas inhalation in Gaza, the Palestine Liberation Organisation says.
Laila al-Ghandour, an 8 months old baby, was declared dead past last midnight due to teargas inhalation yesterday in Gaza. The Palestinian Health Ministry has confirmed that Israel killed 58 other Palestinians on Monday, incl. six children. #Gaza #Nakba70 #GreatReturnMarch pic.twitter.com/szVveMYGrL— Palestine PLO-NAD (@nadplo) May 15, 2018
Palestinian officials reported that at least 2,771 people were injured, including 1,359 by live ammunition.
The violence on Monday marked the deadliest day in the region since the Gaza war in 2014, and marked a dramatic escalation after weeks of protests.
Palestinians had gathered near the border with Israel to demonstrate against the opening of the US embassy in Jerusalem.
Members of the US administration - including US President Donald Trump's daughter Ivanka and her husband Jared Kushner - attended the opening ceremony, less than 50 miles away from the violence in Gaza.
Tuesday also marks the 70th anniversary of the creation of Israel, known as the 'Nakba' or 'catastrophe' by Palestinians.
Palestinian President Mahmoud Abbas declared three days of national mourning in the wake of the violence, as well as a general strike in occupied Palestine.
Images from Gaza on Monday showed Palestinian protesters burning tires and throwing stones, with Israeli troops responding with live fire and tear gas.
Tánaiste Simon Coveney - who is due to brief Cabinet colleagues on the situation - summoned the Israeli ambassador to Ireland to Iveagh House on Tueaday morning "to express Ireland’s shock and dismay at the level of death and injury yesterday on the Gaza Strip".
Minister Coveney also called for restraint from Israel "in the hours and days ahead".
In a statement, a Department of Foreign Affairs spokesperson said: "The ambassador has been informed of Irish demands for an independent international investigation into yesterday’s deaths lead by the UN.
"Our mission in Ramallah reports that emergency responders in Gaza and the strips health services are overwhelmed with the level of casualties. The health system was already facing major challenges due to lack of equipment and essential medicines."
UN Secretary-General António Guterres has also called on both sides of the Israeli-Palestinian conflict to show restraint.
A spokesperson said: "With tensions high and more demonstrations expected in the coming days, it is imperative that everyone show the utmost restraint to avoid further loss of life, including ensuring that all civilians and particularly children are not put in harm’s way."
A White House spokesperson meanwhile, said they believed "Hamas bears the responsibility" - describing it as a "gruesome and unfortunate propaganda attempt".
The Israeli Defence Forces said it would "continue to prevent mass terror attacks, which have largely been orchestrated by the Hamas terror organisation".
The medical charity Médecins Sans Frontières/Doctors Without Borders described the situation in Gaza, calling the violence 'unacceptable and inhuman'.
Marie-Elisabeth Ingres, MSF Head of Mission in Gaza, said: "In one of the hospitals where we are working, the chaotic situation is comparable to what we observed after the bombings of the 2014 war, with a colossal influx of injured people in a few hours, completely overwhelming the medical staff.
"Our teams carried out more than 30 surgical interventions today, sometimes on two or three patients in the same operating theatre, and even in the corridors."
Additional reporting: Jack Quann