An escalated crisis between Egypt and the Hamas government of the Gaza Strip was dampened Tuesday night, as officials met over ways to handle the flood of Palestinians seeking to cross the Rafah border terminal.

Following the May 28 opening of the Gaza-Egypt border, for almost unfettered access to Palestinians except men between 18-40, floods of would-be travelers arrived prepared to cross, overwhelming the terminal.

On the first day of full operations, 530 Palestinians used the terminal crossing both ways, while the second day saw 845 Palestinians pass through the terminal. On Monday, the third day of operations, 722 Palestinians entered or exited Gaza.

The slow process and long lines frustrated officials, while a list of more than 5,000 Palestinians blacklisted from using the terminal sparked anger from Hamas.

Officials traded increasingly headed accusations over who failed in the creation of a mechanism to allow Palestinians to use Rafah, culminating in a late-night meeting between security personnel from both sides.

Following the meeting, the officials announced that a cap of 400 travelers per day would be set on the crossing, and the names of the permitted passengers would be posted one day ahead of travel.

Priority for crossing would be given to medical patients and students, with the added limit that students enrolled at universities outside of Gaza would be given preference over those who had only been accepted but were not yet enrolled.

For patient priority, the officials noted, candidates would have to be examined by an Egyptian medical committee.

While the new mechanisms are expected to ease the crush of people seeking passage at the border, Hamas officials in Gaza have accused Egyptians of failing to meet their pledge to fully open the crossing.

In Cairo, however, officials say they are doing more than enough, noting the move is already a challenge to Israel.