"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.
Obama called for an easing of inflamed Russia-Turkey tensions in a closed-door meeting with Russia's Vladimir Putin on the eve of a climate summit in Paris
Baku accuses Armenian forces of killing Azerbaijani soldier inlatest clash in diputed Nagorny Karabakh region
German Defense Ministry says call for broader coalition against ISIL does not involve Syrian regime forces
'What greater rejection for those who would tear down our world then marshaling our best efforts to save it,' says US president in Paris
Russian President Putin held closed-door talks with his US counterpart Obama on sidelines of UN climate conference in France
'When it comes to the Middle East peace process, the EU continues and will continue to work on this,' European Commission foreign affairs spokeswoman says
Key quotes from opening statements of world leaders at Paris climate summit
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Putin will not meet with Erdogan at Paris climate conference, Kremlin says
Indian Prime Minister Narendra Modi has told that rich nations of their duty to lead climate change fight
An attack blamed on eastern Ugandan rebels has killed 12 in DRC.
Teenager Mohammad Abu Khdeir was kidnapped and burnt to death in 2014. Relatives say the family plans to file a case against the government in the International Criminal Court.
'Those who claim to believe in God must also be men and women of peace,' Pope says
About 150 world leaders, including from the United States, China, India and Russia, converge in French capital
Power cuts in Ghana have been seen as biggest test for John Mahama government ahead of election in 2016