The police said in a statement that new plans would be considered regarding the procession, which Palestinian residents of occupied East Jerusalem see as a provocation.
Israeli police have said they blocked a planned procession by Jewish ultranationalists through parts of Jerusalem's Old City, following warnings that it could reignite tensions that led to a punishing 11-day bombardment of Gaza last month.
The parade, which celebrates Israel's capture of East Jerusalem in the 1967 Mideast war, was underway on May 10 when Israel attacked besieged Gaza after Hamas fired rockets.
Israel's 11-day assault killed some 256 people in Gaza, including 66 children and some fighters, and wounded over 1,900 people. Israel reported 13 deaths on its side before a ceasefire took effect on May 21.
The Israeli assault was preceded by weeks of police aggression in the Old City and in the nearby neighbourhood of Sheikh Jarrah, where Jewish settlers have waged a decades-long campaign to evict Palestinian families from their homes.
The procession, which had intended to go through the Old City's Muslim Quarter, is considered by Palestinian residents of occupied East Jerusalem to be a provocation.
In a statement, police said the proposal to hold the parade later this week was not approved, but new plans would be considered.
The decision was attacked by organisers, who accused police of caving in to pressure from Hamas.
Forced evictions in Sheikh Jarrah
Bezalel Smotrich, leader of the hard-line Religious Zionism party, tweeted a warning to embattled Prime Minister Benjamin Netanyahu “not to give in to Hamas threats."
A further spike in tensions in occupied East Jerusalem or an attack on Gaza, where Hamas has vowed to retaliate, could complicate Israel's shaky politics.
Netanyahu's opponents last week said they have formed a coalition that could remove the prime minister from office after a 12-year term.
The new coalition is expected to be sworn into office in the coming days.
Over the weekend, Israeli police arrested and released a veteran reporter for Al Jazeera who had regularly been covering the Sheikh Jarrah neighbourhood.
And on Sunday, authorities stormed the home of a leading activist in the neighbourhood, arresting her and her brother. The siblings were later released.
Before Muna al Kurd was freed, police briefly clashed with a crowd outside the station, throwing stun grenades and injuring at least 10 protesters.
Sheikh Jarrah is one of the most sensitive parts of occupied East Jerusalem, which is home to sites sacred to Jews, Christians and Muslims and which Israel captured in 1967 and annexed in a move not recognised internationally.
Israel views the entire city as its capital, while Palestinians want East Jerusalem as the capital of their future state.
Sheikh Jarrah has been a major flashpoint in recent violence.
Illegal settlers are using a 1970 law that allows Jews to reclaim formerly Jewish properties lost during the 1948 war surrounding Israel’s creation, a right denied to Palestinians who lost property in the same conflict.
Palestinians who have been coming out in support of families facing evictions have faced Israeli police violence and angry Jewish mobs in recent weeks.