The Hamas-run interior ministry in Gaza said 2,439 people left the territory over the three days, while 1,122 entered and 334 were turned back by Egyptian authorities.
The border was closed again today, a ministry statement said, after "Egyptian authorities informed us of the shutting down of the Rafah crossing."
Egypt originally opened the border for humanitarian cases for two days from Saturday but that was extended for an extra day yesterday.
The United Nations has registered 30,000 Palestinians as "humanitarian cases" seeking to leave Gaza.
At the crossing, long lines of Gazans queued, many carrying heavy suitcases.
Sarah Abu Karesh, a woman waiting at the crossing on Saturday, told AFP she had been trying to leave the territory for months.
"I only came here for a week's holiday and I've been stuck here for 18 months," she said.
The crossing is Gaza's only access point not controlled by Israel, which has maintained a blockade on the territory for nearly a decade.
The border was largely open during the rule of Egyptian president Mohamed Morsi, whose Muslim Brotherhood movement has close ties with the fellow Islamists of Hamas.
But since Morsi's overthrow in 2013, President Abdel Fattah al-Sisi has closed the crossing, with only occasional humanitarian openings.
In 2012, nearly 35,000 travellers used the Rafah crossing each month, according to the UN. In 2015, the monthly average fell to less than 2,400.
Historically many young Gazan studied in Egypt, while many Palestinians visited their families on the other side of the border.
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