Israeli and Palestinian peace activists have been holding protests to mark 40 years since the 1967 Arab-Israeli war.
The Western Wall was part of territory captured in Jerusalem
Protests were taking place in the West Bank and Tel Aviv, but Israeli police prevented a Palestinian conference on the anniversary in Jerusalem.
Palestinian President Mahmoud Abbas said creating a Palestinian state would wipe out the memory of the Arab defeat.
The Six-Day War changed the map of the Middle East, establishing Israel as the region's dominant military force.
Before the war, the 19-year-old Jewish state had been awash with fear, as Arab armies massed on its borders.
Egypt's air force was destroyed by Israeli raids
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 that 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 government marked the anniversary with Jerusalem Day celebrations last month, in accordance with the Hebrew calendar.
Israel has arranged no other official ceremonies for the anniversary and BBC correspondents in Jerusalem say there is a reflective mood and no fanfare.
Several hundred Palestinian activists held a rally in Ramallah in the West Bank, while more protesters marched to the Hawara checkpoint near Nablus - a key local symbol of the Israeli occupation.
In Hebron, about 250 activists of the Israeli anti-settlement group, Peace Now, marched while shouting: "End, end the occupation!"
But Israel banned a Palestinian conference due to be held in East Jerusalem.
Protests at the Hawara checkpoint near Nablus, West Bank
Police deployed around the hotel hosting the conference, entitled "Jerusalem, the capital of the Palestinian state, how to transform slogans into reality", notifying the organisers of the ban.
More events will be held throughout the week, culminating in anti-occupation protests around the world on Saturday.
In an address to mark the anniversary, Mr Abbas remembered the "massive defeat" for the Arabs.
But he also said: "Despite all the difficulties our revolt was equal to this defeat, the memory of which we hope will be erased by ending the occupation of Arab and Palestinian territory and by establishing our independent state."
However, he also warned that recent infighting among Palestinians had left them "on the verge of a civil war".
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.