Rafah is the only major crossing between Gaza, home to 1.8 million Palestinians, and the outside world that does not border Israel, which blockades the strip and allows sporadic passage mainly on humanitarian grounds.
Egypt shut the crossing on October 25 after armed fighters in Egypt's adjacent Sinai region killed 33 members of its security forces in some of the worst anti-state violence since former president Mohamed Mursi was toppled in July 2013.
Since then, Cairo has opened the crossing only twice to allow thousands of Palestinians stranded in Egypt and beyond to return to Hamas-controlled Gaza, Al Jazeera reported.
Hamas has long had ties to the Muslim Brotherhood, which was ousted from power in Egypt when Mursi was overthrown, but its relations with the current Egyptian government are tense.
Maher Abu Sabha, the Hamas-appointed director of crossings, said Rafah would open for two days to allow Gaza residents with serious illnesses to travel to Egypt and beyond for treatment and to allow foreign nationals and students to travel.
An Egyptian official, citing "security reasons", said there was no decision yet to allow the permanent and full opening of the crossing as was the case before October 25.
Hamas's leaders have distanced themselves from violence in Egypt and in Sinai and say they have no armed presence in areas outside Palestinian boundaries.