The three Palestinians were killed on Friday near the Damascus Gate, which is one of the main entrances to the Old City of the occupied East Jerusalem al-Quds.
Malka, who joined the Border Police 15 months ago, is survived by her parents, three sisters and two brothers.
A gun used by one of the attackers reportedly jammed.
Israeli security forces and an ambulance are seen at the scene of an attack outside Damascus Gate in Jerusalem's Old City on June 16, 2017.
"The occupation's crime today in Jerusalem revealed the insistence of the Palestinian Authority on negotiations with the occupation is outside of the national context".
Staff Sgt. Hadas Malka, 23, died shortly after being evacuated in critical condition to Jerusalem's Hadassah Hospital on Mt. Scopus.
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Medics said four people besides the officer were wounded in the incident, two of them moderately and two lightly.
A spokesman for the movement, Hazem Qassem, said the attack was "proof that the Palestinian people are leading a revolution against the enemy".
Since October 2015, Palestinian assailants have killed 42 Israelis, two visiting Americans and a British student, mainly in stabbing, shooting and vehicular attacks.
Others were shot dead during protests or clashes, while some were killed in Israeli air strikes on the besieged Gaza Strip.
"During Ramadan there are large numbers of (Palestinian) youths who enter without permits, they take advantage of Ramadan to be in Jerusalem", he told media at the scene of the attack.
Israeli security services later identified the attackers as 19-year-old Bara Ibrahim Muhammad Saleh; Adel Hassan Ahmad Anakush, 18; and Osama Ahmad Mustafa Atta, 19.
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