Hamas leader Ismail Haniya arrived in Cairo on Sunday to meet the head of Egypt's security services, as speculation mounts that Egypt is seeking to negotiate a deal with Hamas to ease potential violence on Monday.
Sources in Hamas said the meeting comes ahead of major protests expected by tens of thousands of Palestinians on Monday against moving the US Embassy in Tel Aviv to Jerusalem.
Hamas officials have voiced support in recent days for attempts to break the fence into Israel, despite the possibility of it leading to bloodshed.
Arab media have speculated that Egypt, one of only two Arab countries to have a peace treaty with Israel, could ease border restrictions with Gaza and offer economic relief in exchange for protesters not trying to breach the fence.
Fifty-four Palestinians have been killed by Israeli fire since mass protests broke out along the border on March 30. No Israelis have been injured.
The moving of the embassy, a campaign pledge by US President Donald Trump, has infuriated Palestinians, who view the eastern part of Jerusalem as the capital of their future state.
Trump will not attend the embassy opening Monday, but his daughter Ivanka and son-in-law and senior adviser Jared Kushner will.