"We, who hope to return to our lands in Palestine, are planning a peaceful rally this Sunday" at the Lebanese, Syrian and Jordanian borders with Israel as well as the Gaza Strip, Fatah commander in Lebanon Munir Maqdah told AFP.
Maqdah urged Arab states and the UN Interim Force in Lebanon, a 12,000-strong peacekeeping force stationed at Lebanon's southern border with Israel, to "ensure the protection of this peaceful gathering."
He said a committee joining Palestinian and Lebanese factions as well as civil society groups would issue a statement in the coming days detailing the plans for Sunday's protests, which could include setting up tents at Israel's borders.
The 1967 Six Day War saw Israel defeat four Arab armies in six days, and saw it take over east Jerusalem, the West Bank and the Gaza Strip.
It also saw the Jewish state seize the Golan Heights plateau from Syria, and the Sinai Peninsula from Egypt.
The announcement comes after Palestinians marched on Israel's borders with Lebanon, Syria and Gaza on May 15 in a mass show of mourning over the 1948 creation of the Jewish state.
Israeli troops shot dead 10 people and wounded hundreds that day as the protesters attempted to take down barbed wire at the border.