Egyptian foreign ministry officials on Wednesday said the Palestinians have been stuck in Egypt since Israel shut the Rafah crossing into Gaza on 12 July.
Foreign Minister Ahmad al-Ghait has sent an urgent message to Annan asking him to intervene.
Egypt's Red Crescent said it was caring for up to 2000 people at the border, some in tents. Officials say many more Palestinians are stuck in Cairo and other towns.
The Egyptian foreign minister also summoned the Israeli ambassador on Wednesday to strongly demand that Israel "abide by its responsibilities" regarding the dislodged Palestinians.
Israeli authorities regularly close the Rafah entry point for army operations.
Israel said the Palestinian Authority exacerbated the problem by rejecting its offer to use a crossing in Israel and then bring the stranded to Gaza.
The Palestinian officials say they cannot accept the offer that would allow only 200 people a day to reach the wedge of land that houses 1.3 million people.