It was one in two incidents in which three Palestinians armed with semi-automatic weapons and knives attacked Israeli guards in the Old City.
IS issued a statement taking responsibility for the stabbing and shooting attacks Friday evening.
The Times of Israel said, though, that "Israeli officials cast doubt on both claims, saying there was no indication of ISIS involvement, and that the attack did not appear to have been directed by any group".
Three suspected Palestinian attackers were shot dead by security forces, Israeli police said Friday. He said it was a move to "confuse the media and distort the reputation of the Palestinian resistance".
At least three other people were injured in the attacks, two of them Palestinian bystanders who were hit by gunfire, Israeli newspaper Haaretz reports.
Following the deadly attack, Israel immediately ramped up punitive measures, rescinding more than 250,000 permits allowing Palestinians to enter Jerusalem for Ramadan celebrations.
A spokesman for Israel's Shin Bet internal security agency told AFP it was "impossible to corroborate [the IS claim] at this point".
Following the attack, the Israeli army raided Deir Abu Mashal, the village near Ramallah the three perpetrators hailed from, sealing off its entrances and mapping out the homes of the three for demolition. Fatah added that "the global community's silence emboldened Israel to further spill the blood of Palestinians".
On Tuesday, US Secretary of State Rex Tillerson said the Palestinian Authority had agreed to halt payments to the families of slain attackers, including suicide bombers. IS "claims that it carried out the attack are meant to shuffle the cards". On January 8, a Palestinian drove a truck into a group of Israeli soldiers, killing four.
The group warned that "this attack will not be the last".
Instead, an obscure Palestinian group known as the "Groups of Martyr Baha Eleyan" claimed responsibility. Israeli security services say the group has small pockets of support in the Gaza Strip, the West Bank and East Jerusalem, but the majority of Palestinians support rival Palestinian factions Fatah or Hamas.
"A proposal was made, and the topic is still in the stages of study and discussion", a spokesperson for the Israeli police said. She was imbued with a sense of mission of defending the State of Israel.