The attack took place in two adjacent areas near Damascus Gate in Jerusalem's Old City.
Whether or not ISIS had a hand in the attack, the group's Amaq news agency said it wouldn't be its last.
But Hamas, the Palestinian Islamist group that runs the Gaza Strip, dismissed the claim, saying the attackers had come from among its own ranks and the leftist Popular Front for the Liberation of Palestine (PFLP).
The situation remained tense in Israel-occupied West Bank on Saturday, one day after three Palestinians and an Israeli policewoman were killed in attacks in East Jerusalem.
The India game was an aberration, says Mickey Arthur
In a rain-curtailed match at Edgbaston, Team India thrashed Pakistan by 8 wickets with the help of Duckworth and Lewis System. Team India captain Virat Kohli at training ahead of final against Pakistan.
One of the officers, 23-year-old Hadas Malka, was stabbed by one of the assailants as she attempted to reach for her weapon.
Four other people were injured in Friday's attacks, including another Israeli police officer and a Palestinian passer-by who had no involvement in the incident.
In a briefing with journalists Jerusalem police commander Yoram Halevy said the three men involved in the attack were aged between between 18 and 19 years old and had entered Jerusalem from the West Bank.
The Shin Bet said they had been previously been implicated in "terror activity".
The army sealed off the assailants' home village while troops went house to house, arresting two youths before leaving after a number of hours.
Elsewhere in the West Bank, a Palestinian "attempted to stab an Israeli" north of Hebron early Saturday, the army said.
US Open leaderboard 2017
Spieth never wandered into negative numbers on the front nine, posting only two birdies the entire day (he has six on the week). The Englishman shot a one-under 71 but had to fight back from two bogeys and a triple bogey in his first six holes.
A second Israeli officer was wounded.
The Prime Minister's Office then made a decision to halt all special Palestinian entry permits to Israel issued for Ramadan, though worshipers from within the Green Line can continue to access the Aksa Mosque compound as usual. A spokesman for the movement, Hazem Qassem, said the attack was "proof that the Palestinian people are leading a revolution against the enemy".
The al-Aqsa Mosque compound is a flashpoint Islamic site, which is also holy to Jews.
"The attack was carried out by three Palestinians, two PFLP members and a Hamas member", said Hamas spokesman Sami Abu Zuhri, adding that IS claims that it carried out the attack are meant to sow confusion.
Israeli security officials did not respond immediately to requests for comment on what the SITE intelligence monitoring group described as the first time Islamic State had claimed responsibility for an attack in Israeli-controlled territory, nor on the attackers' affiliation.
Stage set for wide open run at US Open title
This week, so far, you've had to make birdies your friends, even if the course is playing 7,800-plus yards. It's a nice comeback for Casey after he triple bogeyed the par-5 14th and shot 38 on the back nine.