The Palestinian Ministry of Health identified the slain attackers as Adel Hasan Ahmad Ankoush, 18; Baraa Ibrahim Salih Taha, 18; and Osama Ahmad Dahdouh, 19.
The area around Damascus Gate was sealed off in the hours after the attack, with a few youths throwing fireworks at security forces.
If IS's claim of involvement was true, it would be its first direct action against Israel.
A wave of Palestinian street attacks began in October 2015 but has since slowed.
At one location, two Palestinians were shot dead after opening fire at a group of Israeli police officers.
The names differ from those reported by ISIL, which said the attack was carried out by three brothers by the names of Abu al-Bara'a al-Maqdisi, Abu Hassan al-Maqdisi, and Abu Rabah al-Maqdisi, AFP reported.
Staff Sgt. Hadas Malka, 23, died shortly after being evacuated in critical condition to Jerusalem's Hadassah Hospital on Mt. Scopus. Palestinians say the Israeli measures are aimed at paving the way for the Judaization of the city.
In their village of Deir Abu Mashal, near Ramallah, relatives of the three denied any connection to the Islamic State or the other groups.
Another Palestinian man from Hebron was also injured by Israeli security forces, despite playing no role in the attacks.
BJD extends support to Kovind's name for President
Venkaiah Naidu and Rajnath Singh met Congress president Sonia Gandhi last week, the Congress leader said. Mr Naidu and Mr Singh are also likely to meet CPI-M general secretary Sitaram Yechury later today.
"This is an obvious form of collective punishment, it is not acceptable - all those who are using these permits to meet with their families and to be with them during Ramadan are doing so during the month, because most of the year they are not able to do so", Touma-Suleiman said.
Inside the Old City shops were open but the atmosphere was subdued and numbers of people much lower than normal.
It claim the entire city as its indivisible capital but the Palestinians claim its eastern sector as the capital of their promised state.
Some Israeli media later said that ISIS had claimed responsibility.
Major General Yoav Mordechai, the head of COGAT, the Israeli defence ministry agency responsible for civilian affairs in the Palestinian territories, said the 250,000 family visit permits were cancelled in response to "encouragement to terrorism" by Palestinian President Mahmud Abbas's Fatah movement.
Israeli figures pointed the blame at Palestinian leaders.
Netanyahu, however, did not revoke the permission given to Palestinian men aged over 40 from the West Bank to enter Jerusalem for Friday prayers, police said.
Israel is a prominent subject in ISIS's propaganda output, with the group regularly stating that it seeks to take over Jerusalem, where the third-holiest site in Islam-the Haram al-Sharif, or Noble Sanctuary-and the most holy in Judaism-known to Jews as the Temple Mount-is located. "I am not speaking about territories bordering the State of Israel, but within the State itself", he said in a speech at Tel Aviv University.
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