"We reiterate the importance of the provision of urgent humanitarian aid and stand ready to continue supporting those civilians most in need in Gaza... ensuring that such assistance is not abused by terrorist organisations," the statement said.
"It is crucial to prevent regional escalation" of the conflict, it added.
The joint statement was adopted two days ahead of an emergency video summit of the member nations called by European Council President Charles Michel.
"The European Union condemns in the strongest possible terms Hamas and its brutal and indiscriminate terrorist attacks across Israel and deeply deplores the loss of lives," it said, while also calling for "the protection of all civilians at all times."
EU leaders say they "remain committed to a lasting and sustainable peace based on the two-state solution through reinvigorated efforts in the Middle East Peace Process."
FILE -- European Council President Charles Michel (C,L), European Parliament President Roberta Metsola (C) and European Commission President Ursula Von der Leyen (C,R) pay tribute to the victims of the Hamas attacks in Israel, at the European Parliament on October 11, 2023.
The joint position comes days after a visit to Israel by European Commission President, which drew criticism from some diplomates and European deputies.
Addressing von der Leyen in a message on X, formerly Twitter, French MEP Nathalie Loiseau wrote Saturday: "Yes, Israel has the right to defend itself against bloodthirsty terrorists."
"You are forgetting an important message: Israel must respect international humanitarian law."
The death toll from Israeli strikes on the Gaza Strip has surged to at least 2,670 since Hamas's bloody attack on southern Israel last week, the Gaza health ministry said Sunday.
More than a million Gazans have been forced to flee their homes after Israel warned them to move out of the north of the Palestinian coastal enclave.
Another 9,600 people have been wounded as Israel continues its blistering air campaign on targets in the Gaza Strip, the Hamas-controlled ministry said.
Israel declared war on the Islamist group last Sunday, a day after waves of fighters broke through the heavily fortified border and shot, stabbed and burned to death more than 1,400 people, most of them civilians.
Around 120 hostages are also being held in the Gaza Strip from the initial attack.