"There is no justification for the closure of the Rafah crossing," Hamad al-Raqb, a spokesman for the protesters, said in a speech marking the beginning of a four-day sit-in.
"It is unbecoming of the historic relations between Egyptians and Palestinians," he insisted.
Leading Hamas figures and MPs attended the launch ceremony.
Egyptian authorities have tightened their control over the border with the Hamas-run Gaza Strip since last July's ouster of elected president Mohamed Morsi by the Egyptian army.
In recent weeks, Egypt has repeatedly closed the Rafah crossing, which – due to an ongoing, eight-year Israeli siege – represents Gaza's only window to the outside world.
The Egyptian army has also launched a campaign aimed at destroying the network of tunnels linking Gaza to Egypt's Sinai Peninsula, which in recent years had been used to bring vital commodities into the besieged coastal enclave, home to nearly 2 million Palestinians.
Hamas, an ideological offshoot of the Muslim Brotherhood, the group which propelled Morsi to power in the 2012 elections, has controlled the Gaza Strip, since 2007.
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The protests were called to demonstrate against the government of President Joseph Kabila who many in Congo fear is manoeuvering to stay in office indefinitely beyond the end of his term in December.
"It is incomprehensible and unacceptable, it was a mistake," Renzi told Italian radio.
The hold up also threatens to torpedo next week's planned visit to Brussels by Canadian Prime Minister Justin Trudeau to sign the deal.
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