Israeli and Palestinian peace activists are planning protests to mark 40 years since the Arab-Israeli war of 1967.
In Tel Aviv, protesters will erect a dummy checkpoint to portray restrictions on West Bank Palestinians.
But in Jerusalem, Israeli police prevented a Palestinian conference to mark the anniversary from taking place.
The so-called Six-Day War changed the geo-political map of the Middle East, establishing Israel as the region's dominant military force.
Air strikes
Before the war, the 19-year-old Jewish state had been awash with fear, as Arab armies massed on its borders.
UN peacekeepers had been expelled from the Sinai, and Egypt had closed the Red Sea to Israeli shipping.
In an extraordinary showdown on the eve of war, Israeli generals swore and shouted at the prime minister that Israel had to strike first to be sure of victory.
The conflict began with air strikes which destroyed much of Egypt's air power on the ground.
By the end of the fighting, Israel had defeated the armies of Egypt, Jordan and Syria.
It captured territory three times the size of the country as it was on 4 June.
The Golan Heights and Palestinian territory in the West Bank, Gaza and East Jerusalem remain under its control to this day.
The Israeli cabinet is to meet this week to discuss whether to restart peace talks with Syria.
Israeli Pensions Minister Rafi Eitan told local radio that Israel should consider the Golan Heights as a bargaining chip, if Syria was sincere about negotiation.
Egyptian reluctance
Simultaneous rallies are to be held in Tel Aviv and East Jerusalem, while the anti-settlement campaign group Peace Now is planning a protest in the divided West Bank city of Hebron.
And in the West Bank city of Ramallah Palestinians were expected to observe a minute's silence at 0900 GMT.
But Israel banned a Palestinian conference due to be held in East Jerusalem.
Police deployed around the hotel hosting the conference, titled "Jerusalem, the capital of the Palestinian state, how to transform slogans into reality", notifying the organizers of the ban.
More events will be held throughout the week, culminating in anti-occupation protests around the world on Saturday.
The Israeli government marked the anniversary with Jerusalem Day celebrations last month according to the Hebrew calendar.
But in Egypt there are no official events to mark the anniversary or the sacrifice of those who died - just the occasional newspaper article recalling what happened.
Egypt had been defeated and even if the country eventually recovered the Sinai peninsula, which it lost in 1967, many Egyptians remain reluctant to discuss the war, says the BBC's Owen Bennett Jones in Cairo.
The reticence is in part a reflection of Egypt's demographics, BBC correspondent says. Most Egyptians had not even been born when the 1967 war took place.
PHOTO CAPTION
Israeli soldiers after capture of Jerusalem’s western wall in 1967