The Israeli security services also raised doubts about the veracity of the IS claim -- its first for an attack in Jerusalem -- which came with the jihadists facing defeat in their Iraq and Syria bastions.
Three Palestinians attacked officers just outside the walled Old City in annexed east Jerusalem late on Friday before being shot dead by security forces, Israeli police said.
In an online statement, IS said jihadist fighters had targeted a "gathering of Jews", warning that "this attack will not be the 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 those of the leftist Popular Front for the Liberation of Palestine (PFLP).
The assault took place as tens of thousands of Palestinians held night prayers at the nearby Al-Aqsa mosque compound, Islam's third-holiest site, on the third Friday of the holy fasting month of Ramadan.
According to police, two assailants opened fire on a group of officers who returned fire, and a third stabbed the border policewoman a short distance away before being shot.
Policewoman Hadas Malka, a 23-year-old staff sergeant major, was taken to hospital in critical condition and later died of her wounds.
Four other people were wounded in the incident, including two Palestinians from east Jerusalem and one from the West Bank city of Hebron.
'Muddy the waters'
In its statement, IS said the attack was "revenge for the religion of Allah and the sanctities of the violated Muslims".
"Let the Jews watch for the demise of their state at the hands of the soldiers of the caliphate," the statement said.
Hamas spokesman Sami Abu Zuhri said the IS claim was an attempt to "muddy the waters", adding that the attack was carried out by "two Palestinians from the PFLP and a third from Hamas".
The killing was "a natural response to the crimes of the occupier," he said, echoing the language used by Hamas after other recent attacks against Israelis.
A spokesman for Israel's Shin Bet internal security agency told AFP it was "impossible to corroborate (the IS claim) at this point."
The Israeli army said the assailants appeared have acted independently, like many of the attackers in a wave of unrest that has rocked Israel and the occupied territories since October 2015.
Most of the attacks have been carried out by "lone wolves", some only in their teens, and Israel has dubbed the violence "popular terrorism."
"A preliminary army intelligence evaluation found no evidence of them belonging to any group, rather they appear to have been a typical popular terror squad," an army spokeswoman said.
Hamas and the PFLP identified the three assailants as Bara Ata, 18, Osama Ata, 19, and Adel Ankush, 18, all from the village of Deir Abu Mashal near the West Bank city of Ramallah.
The Shin Bet said they had been implicated in previous "popular terror activity".
The PFLP said Bara and Osama Ata had recently been released from several months in Israeli prison.
The army sealed off the assailants' home village.
Elsewhere in the West Bank, a Palestinian "attempted to stab an Israeli" north of Hebron early Saturday, the army said.
The Israeli was lightly wounded and the assailant taken in for questioning.
Ramadan relaxation curbed
Israel had eased restrictions on the entry of Palestinians from the West Bank to Jerusalem for Ramadan.
But after Friday's attack, Prime Minister Benjamin Netanyahu decided to cancel permission for Palestinians from the West Bank of all ages to visit family members in Jerusalem and Israel, police said.
Permits for Friday prayers for women of all ages and men aged 40 and over are to remain in place.
The unrest that broke out in October 2015 has claimed the lives of 272 Palestinians, 42 Israelis, two Americans, two Jordanians, an Eritrean, a Sudanese and a Briton, according to an AFP tally.
Israeli authorities say most of the Palestinians killed were carrying out knife, gun or car-ramming attacks.
Saturday was the first time IS had claimed an attack inside Israel or annexed east Jerusalem.
The jihadist group has a major presence across Israel's southern border in Egypt's Sinai Peninsula, from where it has claimed several rocket attacks from into Israel.
