RAFAH, Gaza Strip — For most of the past decade, Egypt has been a quiet partner with Israel in a blockade on the Hamas-ruled Gaza Strip that has stifled the economy and largely blocked its 2 million people from moving in and out of the territory. But after a three-year crackdown, there are signs that Egypt is easing the pressure in a step to repair its shattered ties with the Islamic militant group.

In recent months, Cairo has increased the number of people allowed to exit through the Rafah border crossing, Gaza’s main gateway to the outside world. It also has begun to allow Gaza to import commercial goods through Rafah for the first time since 2013 and sent public signals that it is interested in improving relations.

“There is a ball of hope that was thrown by Egypt,” said Ashraf Jomaa, a Gaza community leader who has taken part in recent meetings with Egyptian officials to discuss the changing ties. “The question is how we, the Palestinians, shall catch that ball and develop the hope.”

The changes, while still in their infancy, mark a significant departure from what has been a tough Egyptian crackdown since the military ousted its then-president, Mohammed Morsi, in 2013. Hamas, an offshoot of Morsi’s Muslim Brotherhood, enjoyed close relations with him and quickly fell into disfavor with the new government.

Under President Abdel-Fattah el-Sissi, the former military chief who ousted Morsi, Egypt all but destroyed a once-thriving network of cross-border smuggling tunnels used by Hamas — robbing the group of its main economic lifeline and a key source of weapons.

Targeting Islamic militant groups in Egypt’s northern Sinai Desert, it also destroyed hundreds of homes in the volatile border area to create a “sterile zone.” Egypt’s state-run media have repeatedly accused Hamas of collaborating with militants in Egypt, a charge the group denies.

The crackdown has had a devastating effect on both sides of the border.