Locals said police had placed barbed wire across the entrance to the border and closed the gates with chains, leaving hundreds of Palestinians stranded on both sides of the fence.
Islamist gunmen abducted seven Egyptian security forces on Thursday and have demanded the release of imprisoned militants in exchange for the men. Three of those abducted have worked at the Rafah crossing, sources said.
The police at Rafah are calling on Egyptian President Mohammed Morsi to free their colleagues, the sources said.
Hardline Islamist groups based in North Sinai have exploited the collapse of state authority after the 2011 uprising that toppled former President Hosni Mubarak to launch attacks across the border into Israel and on Egyptian targets.
The gunmen are seeking the release of members of Islamist group Al-Tawhid wal Jihad who were convicted of carrying out attacks in North Sinai in 2011 that killed six members of the security forces and a civilian, a security official said.
Last September, a court sentenced 14 members of the group to death and another four to life imprisonment.
Last August, 16 Egyptian border guards were killed in an attack blamed on militant Islamists who hijacked an armored vehicle that they smashed through the border into Israel. They were killed by Israeli forces.
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