Egypt last opened the crossing in August
Palestinian officials in Gaza say the Rafah crossing with Egypt is being opened for two days to let students, pilgrims and medical cases leave.
The border has mainly been shut by Egypt since Hamas militants seized control of the territory in June 2005.
An Egyptian official said 3,000 Gazans had registered to leave this time.
In the West Bank meanwhile a Palestinian was killed by troops after throwing a petrol bomb at soldiers, Israel's military said.
The army said the Palestinian was shot dead near the Jewish settlement of Yitzhar, which has become a flashpoint for violence.
Last week about 100 settlers rampaged through the nearby Palestinian village of Asira al-Qabaliya after an intruder stabbed and wounded a child in Yitzhar.
Hamas officials in Gaza said about 650 people would be allowed through Rafah to go on pilgrimage to Saudi Arabia, AFP news agency reported.
The others are reported to be students at foreign universities and medical patients seeking treatment abroad.
The crossing was last opened for two days by Egypt at the end of August.
Israel has also sealed its border crossings with the coastal territory, allowing in only humanitarian aid and basic supplies.