"The EU condemns the murder of these four young Israelis, as well as any praise or incitement for terrorist acts," a spokesperson of the European External Action Service (EEAS), or the EU's diplomatic service, said in a statement.
"There can be no justification for such a crime," the spokesperson said, "the EU will continue to work with those who seek peace and denounce those who pursue violence and terror."
Palestinian media identified the perpetrator as Fadi al-Qanbar from East Jerusalem's Jabel Mukaber neighborhood.
Israel's police spokeswoman Luba Samri said that the incident -- which took place in Armon Hanatziv, a popular promenade that overlooks East Jerusalem's Old City -- was a "terrorist attack," although the investigation has yet to be concluded.
At noon, the assailant drove his truck into pedestrians, killing four soldiers, three of them women, and wounding 15 more, Samri said.
The attack was one of the deadliest amidst a more than yearlong wave of violence. Last June, two gunmen killed four persons at a trendy recreation compound in Tel Aviv.
An ongoing wave of violence in the West Bank and Israel has claimed the lives of at least 235 Palestinians and 34 Israelis since September 2015.
Israeli leaders accuse the Palestinian National Authority of "inciting" the unrest, while the Palestinians say it is the result of nearly 50 years of Israeli occupation of the West Bank and the Gaza Strip, home to more than five million Palestinians, where they wish to establish their state.