RAFAH, Gaza Strip — For most of the past decade, Egypt has been a quiet partner with Israel in a blockade on the Gaza Strip, introduced after a violent takeover by the Hamas terrorist organization. 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 Palestinian 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.”

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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.

The olive and palm trees that once lined the 40-kilometer (25-mile) road from Rafah to el-Arish, the provincial capital of North Sinai, have been razed and even small bushes have withered.

The road is littered with checkpoints, tanks and mobile artillery units, manned by anxious young soldiers. In the town of Sheikh Zuwaid, where travelers used to stop to buy Egyptian mobile phone cards and snacks, stores were gutted, their doors bombed out. The bullet-riddled houses above them were turned into military positions, with sandbags covering the windows and snipers stationed on the roofs. The US-based Human Rights Watch estimates that thousands of people have been displaced — most of whom moved either elsewhere in town or to el-Arish.

In Gaza, years of Egyptian restrictions, coupled with an Israeli blockade and three wars between Hamas and Israel, have devastated the economy and weakened Hamas.

The UN and other international bodies estimate unemployment to be 43 percent, and Hamas has struggled to pay the salaries of the 40,000 police and civil servants it hired after seizing Gaza in 2007.

An Israeli naval blockade, which Israel says is needed to prevent arms smuggling, means that most goods enter Gaza through Israeli-controlled cargo crossings. While most consumer goods are freely available, prices of fuel, cigarettes and other items have spiked because of limited supplies. Construction materials, badly needed to rebuild damage from a 2014 war, remain in short supply.

But Egypt’s recent turnaround has begun to bring some relief. In the past six months alone, Rafah crossing has been opened more than 40 days, compared to just 26 in all of 2015, allowing thousands of people to leave for jobs, medical care, family visits and studies abroad.

Last month, it allowed a top Hamas leader, Ismail Haniyeh, to travel abroad for the first time since Morsi was toppled. In addition, it allowed a Malaysian official to enter Gaza to meet with Hamas officials. In another first, it allowed cargo to be shipped into Gaza through Rafah, including 40 new cars, painting materials and tar.

In recent months, Egypt has invited three delegations of businessmen, academics, community leaders and journalists from Gaza for semiofficial conferences in Cairo. Participants said the issue of creating a trade zone between Gaza and Egypt was raised. Hamas has begun paving a patch of land on the Palestinian side of the crossing for what local media say will be an area to contain more imports from Egypt.

At a recent meeting, Egyptian officials said they were interested in “opening a new chapter” with Gaza, said one official, who was not allowed to be identified under the briefing guidelines. “We are still evaluating the situation, and this is a long dialogue until we reach better relations.”

Hamas has welcomed the moves, saying it is ready to shutter the tunnels if commercial activities increase above-ground. Senior Hamas official Mahmoud Zahar said, “If the (Rafah) crossing opened commercially, what’s the need for the tunnels?”

But Hamas, an armed group sworn to Israel’s destruction, has repeatedly seen its hopes dashed as it tries to emerge from isolation. It remains unclear how far Egypt is willing to help the group, especially if it continues using tunnels to bring in arms.

“If the tunnels are used by the Palestinian resistance, then this is something else that doesn’t harm the Egyptian security,” Zahar said.

Beverly Milton-Edwards, a visiting fellow at the Brookings Doha Center, said any Egyptian moves toward Gaza are to promote its own national security interests. With Egypt still locked in battle against Islamic extremists in Sinai, any change will likely be slow and cautious, and could depend greatly on Hamas’ own actions.

Egypt still fears Sinai militants will use the tunnels to escape or to bring in explosives from hard-liners within Hamas’ armed wing.

“The signaling of intent is carefully calibrated to remind the Gaza government of the levels of control and power that Egypt can exert positively or negatively,” Milton-Edwards said. “If there is not enough evidence of compliance by the Hamas government then Cairo will not hesitate to halt all alleviating measures.”