In a stuffy basketball stadium in southern Gaza, the stands are packed. Young people, the elderly and families sit on blue and yellow plastic seats, their eyes fixed on the court.

But there is no game, and these people are not fans but hopeful travellers. The crowds carry suitcases with them and have been waiting to leave, some of them for months.

In the middle of the cavernous room, an official sits at a wooden table with a list of people who have been approved that day to exit into Egypt. When he calls a name, that person can join a bus heading across the border.

A 60-year-old woman said she had been attempting to get permission to leave from the Egyptian authorities for a year and four months. Although a Palestinian, she has lived for the past three decades in Germany, where she has citizenship, but came back for what she hoped would be a short visit to her parents.

“I registered to travel [out of Gaza] a week after I arrived. This is the first time I’m on the list,” said Mufida, holding up her German passport. “No one’s name has been called out today,” she added.

Q&A What is the history of the Palestinian reconciliation efforts? Show The two main Palestinian parties – the Fatah faction of Palestinian Authority president Mahmoud Abbas and the Islamist militant group Hamas – have run separate governments in the West Bank and Gaza respectively since 2007. The situation emerged after Hamas defeated Fatah in parliamentary elections in 2006. Fatah refused to recognise the result, leading to a near-civil war that saw Hamas push Fatah out of Gaza. Numerous attempts at reconciliation have ensued but the latest effort looks the most serious yet. The issue of who controls the borders and runs government ministries is a key test, not least in loosening the Israeli blockade on Gaza, imposed after Hamas took control.

Responsibility for land border crossings – in a coastal strip without a commercial sea port or airport – is crucial, as Palestinians and goods can only cross by these checkpoints. Both Egypt and Israel will want to ensure that no arms reach Hamas and other groups.

Mufida, who asked to give only her first name, received a call last week that she had a permit to leave but would need to wait for her name to be called. For four days she has waited at the stadium. Rumours swirl that several thousand dollars in bribes will get you across, but Mufida smiled and said she did not have the cash. “Nobody should come back here,” she said. Her seven children are waiting for her in Germany.

A decade-long blockade on Gaza, the tiny strip of land surrounded by Israel, Egypt and the Mediterranean, has led to the collapse of its economy and the enclave is regularly referred to as an open-air prison. It had been hoped that close to two months of protests, sparked by anger and desperation, would lessen this crisis for two million Palestinians. Since late March, tens of thousands have gathered weekly along the frontier with Israel to demonstrate against the conditions they live under.

Amid an international outcry and calls for investigations, Israeli fire has killed more than 110 people and thousands of others have been shot, mostly in the legs, according to health officials.

The most important thing for the protest was to break the siege, to live in freedom and dignity Gaza academic

The movement peaked on Monday, when an estimated 40,000 descended on the frontier, many throwing stones towards Israeli forces stationed on sandbanks behind the fence. There were attempts to breach the perimeter, although none succeeded, and many more of the wounded were shot dozens of metres back from the fortified fence, including paramedics.

Monday’s gatherings were focused on dismay over the opening of the US embassy in Jerusalem on the same day. And the protest organisers have called the movement the “Great March of Return”, demanding refugees and their descendants – two-thirds of Gaza’s residents – be allowed to return to homes lost in the 1948 war surrounding Israel’s creation.

But the primary goal was ending the blockade, according to Mkhaimar Abusada, a political scientist at Gaza’s Al-Azhar University. “That is the number-one aim of the protest, even if the slogan is the Great March of Return,” he said. “The most important thing for the protest was to break the siege, to live in freedom and dignity, to live a better life.”

Israel says it is forced to control access to the territory for security reasons, although the UN sees the blockade as collective punishment.

A Palestinian protester in clouds of tear gas. Photograph: Mohammed Saber/EPA

Egypt, which accuses Gaza’s rulers, Hamas, of smuggling out fighters and weapons, only periodically opens the strip’s southern Rafah crossing. Trucks carrying cement and wood were seen there last week, and Cairo said the exit would remain open for the month of Ramadan – the longest uninterrupted period since 2013.

The past few days have seen roughly 500 people cross per day, although thousands remain on lists. Travel is mostly restricted to patients and students enrolled in universities abroad, as well as dual citizens.

Israel, however, has not significantly changed access at its crossings. It says Palestinians ransacked one crossing, although it later sent some medical supplies into Gaza through it. Hamas rejected the truckloads of aid, calling it a propaganda stunt. Another four trucks filled with medical supplies from Jordan were allowed to cross on Friday, the UN said, although access remains severely restricted.

The protests have failed to elicit much support in Israel, where the bloodshed has been framed in large part as a response to a potential security threat to Israelis. One Israeli soldier has been injured since protests began. A poll conducted this month found 83% of Jewish Israelis believed the army’s open-fire policy was justified.

Israel’s government blames Hamas for the deaths of people killed by Israeli forces, saying it has pushed civilians into the line of fire. Defence Minister Avigdor Liberman called Hamas a “bunch of cannibals”.

Yehuda Shaul, one of the founders of Breaking the Silence, an anti-occupation Israeli human rights group run by military veterans, said most of Israeli Jewish society had “sadly enough, bought into the talking points of the government”.

“It was really devastating to see the response of mainstream Israel, so to speak, on this,” he said.

Voices of outrage have been largely muted and sidelined. Small protests across the country condemning the army’s use of live fire have barely reached the low hundreds. “There was a voice of dissent. It’s a minority, but it’s there,” Shaul said. “There is a voice and we are proud of it, but we are a minority.”