Lebanese and Palestinian activists had planned to protest at the border with Israel but Lebanon's army banned any gatherings at the frontier, fearing a repeat of last month's violence on the anniversary of Israel's 1948 creation.
On May 15, clashes between protesters and Israeli soldiers left six dead on the Lebanese border and four more in the Golan Heights at the ceasefire line between Syria and the Jewish state.
Twenty protesters on Sunday in the keffiyeh Arab headdress tried to stage a rally in Adaisseh, facing the Israeli kibbutz of Misgav Am, but were quickly dispersed by Lebanese police and soldiers, an AFP photographer said.
The army on both sides of the fence were on alert, as was the United Nations Interim Force in Lebanon (UNIFIL).
Shops were closed in Lebanon's 12 Palestinian refugee camps, where black flags of mourning were hoisted, as the army reinforced its presence, particularly in the south.
Lebanese soldiers manned roadblocks on roads to the border.
During the Six-Day War, Israel seized the Sinai peninsula, which it returned to Egypt in 1982, Syria's Golan Heights, the West Bank including east Jerusalem, and the Gaza Strip, from which Israeli troops and settlers withdrew in 2005.