Police said the incident, which took place on Israeli Independence Day, involved two suspected attackers. One fired a rifle while the other attacked people with an axe or a knife, police said.
The suspects have still not been apprehended, according to Israeli police, who urged the public to stay away from the scene.
“At this point, security crossings have been deployed on various roads, together with a helicopter, searching for a vehicle that was seen fleeing the scene,” a police spokesperson said.
Pictures from the scene showed multiple emergency vehicles including ambulances and motorcycles.
Two of the wounded have arrived at Beilinson hospital, the hospital said. One is in critical condition and one in serious condition, it said.
“This is a very difficult event. When we arrived at the place we noticed that it was a complex scene,” Alon Rizkan, a paramedic from Israel’s emergency response service Magen David Adom (MDA), said in a statement.
All three of the dead were men in their 40s, Rizkan said.
Two men, aged 60 and 35, are seriously injured, Rizkan said. A 40-year-old man was moderately injured and a 23-year-old man was lightly injured fighting the attackers, he added.
The attack marks the latest in a series of violent incidents that have put Israel and the Palestinian territories on edge in recent weeks.
Dozens have died in attacks in Israel and the West Bank since March 22, according to a CNN count.
In one incident, two people were killed and more than a dozen others were wounded in a shooting at a bar in a busy area of Tel Aviv.
Palestinian Authority President Mahmoud Abbas condemned Thursday’s violence, his office said in a statement.
“The killing of Palestinian and Israeli civilians only leads to a further deterioration of the situation at a time when we all strive to achieve stability and prevent escalation,” Abbas said in the statement.
Abbas warned against Jewish settlers using the incident as an excuse “to carry out attacks and reactions against our Palestinian people.”
He added that the “lasting, comprehensive and just peace is the shortest and best way to provide security and stability for the Palestinian and Israeli peoples and the peoples of the region.”
Late Thursday, Palestinian militant groups in Gaza, Hamas and Islamic Jihad, praised the suspected terror attack, without explicitly taking credit for it.
Hamas spokesman Fawzi Barhoum linked the attack to clashes at Jerusalem’s al Aqsa mosque compound.
“This is a brave and heroic act that comes as a natural response to the violations of the occupation against al Aqsa Mosque,” he told CNN, referring to the presence of Israeli security in the compound.
The attack “sends a message to the occupation that all its crimes and violations will only return to it,” he said, referring to Israel. “Our natural right is for our people to respond to the crimes of the occupation, to deter it, and to defend our rights. Today, the occupation is paying the bill for its violations.”
Islamic Jihad political bureau member Muhammad Hamid Abu Al-Hassan congratulated the attackers.
“The desecration of the occupation army and settler gangs of al Aqsa Mosque crossed all red lines, and our people will continue to respond to this aggression,” he said, a nod to clashes that occurred at the compound on Thursday.
Only Muslims are allowed to visit the holy site, called the Temple Mount by Jews and Haram al-Sharif or Noble Sanctuary by Muslims, during the last 10 days of Ramadan each year. Groups of Israeli Jews began visiting again on Thursday.
US State Department spokesperson Ned Price said that Thursday’s suspected terror attack appears to be “the latest in a what has been a string of despicable terrorist attacks that have rocked Israel in recent weeks.”
“We saw them in advance of this holy period — the confluence of Easter, of Passover, of Ramadan. We saw them in advance of the Negev Summit. And if this is what it appears to be, it is something that we would condemn in strongest terms,” Price said.
“Our commitment to our Israeli partners, to Israel’s security, that is ironclad, and we’ll provide any and all assistance that may be required in this case,” he added.
CNN’s Jennifer Hansler and Jorge Engels contributed reporting.