The decision was taken “to alleviate the suffering” of residents in the Palestinian enclave, Sisi said on Facebook on Thursday.
The Rafah crossing is Gaza’s only gateway to the outside world not controlled by Israel but Egypt has largely kept it closed in recent years, citing security threats.
It is usually only open for a few dozen days a year.
About 60 Palestinians were killed by Israeli fire on the Gaza border this week, with the victims described by Egypt’s foreign ministry as “martyrs”.
A total of 114 Gazans have been killed since 30 March, in the run-up to the opening on Monday of the US embassy in Jerusalem.
Egypt has relations with both Israel and Hamas, the rulers of Gaza, and Cairo plays a key role in easing tensions between the two sides and alleviating the pressure on the enclave’s 2 million residents.
The Hamas leader, Ismail Haniyeh, paid a brief visit to Egypt on Sunday, where he met the director of the country’s intelligence services, Abbas Kamel.
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