The deal seemed on the verge of unraveling. Hamas had accused Israel of failing to keep its side of the bargain and Israel was threatening to resume its lethal onslaught on the Gaza Strip.

That was the point at which a Qatari jet landed at Israel鈥檚 Ben-Gurion International Airport on Saturday. Negotiators aboard set to work, seeking to between Israel and Gaza鈥檚 Hamas rulers before it fell apart and scuttled weeks of high-stakes diplomatic wrangling.

The first public visit by Qatari officials to Israel marked an extraordinary moment for the two countries, which have . It also underscored the major in bridging differences between the enemies.

鈥淭his is something we鈥檝e never seen before,鈥� Yoel Guzansky, a senior fellow at the Institute for National Security Studies in Tel Aviv, said of the Qataris鈥� stay in Israel. 鈥淚t鈥檚 the only external actor in the world with that much leverage on Hamas, because of its many years of support.鈥�

The weekend mission was successful, and most of the team jetted home. But several Qatari mediators stayed behind to work with Israeli intelligence officials on extending the four-day truce, which ends Tuesday morning, according to a diplomat briefed on the visit who spoke on condition of anonymity because of the sensitivity.

With its close ties to the United States 鈥� it hosts the between Europe and Japan 鈥� its communication with Israel since 1995 and its support of blockaded Gaza to the tune of what estimates suggest is more than $1 billion since 2014, Qatar is uniquely positioned to break deadlocks in the cease-fire talks, which also involve the U.S. and Egypt.

鈥淲e need Qatar,鈥� Guzansky said of Israel, noting that other Arab countries increasingly have interests in Israel and are normalizing their relations. 鈥淨atar is seen as the only player in the Arab world that is loyal to the Palestinian cause.鈥�

The emirate has hosted an overseas since 2012, allowing Qatar to wield some influence over the militant group鈥檚 decision-makers. Top Hamas officials, including the group鈥檚 supreme leader, Ismail Haniyeh, live in Qatar.

Qatar says Hamas鈥� political office in its capital, Doha, came about at the request of U.S. officials who wanted to establish a communication channel, just as Doha had hosted Taliban offices during America鈥檚 20-year war in Afghanistan.

Qatari officials say they are guided by a desire to reduce conflict, though their ties with a range of Islamist groups, including Hamas, the Muslim Brotherhood in Egypt and the Taliban have drawn criticism from Israel, some U.S. lawmakers and .

鈥淭his is soft power on steroids, mobilized for America鈥檚 interest,鈥� said Patrick Theros, a former U.S. ambassador to Qatar. 鈥淗osting organizations which the United States cannot be seen talking to is part of this policy.鈥�

The wealthy Gulf Arab state with a native population of just 300,000 has leveraged its strategic location and tremendous natural gas riches to wield political influence and project soft power around the world, including as host of the 2022 World Cup.

In the Israel-Hamas hostage negotiations, Qatari mediators, joined by those from Egypt and the U.S., faced the task of getting the warring sides to put faith in diplomacy when trust was sub-zero.

Over the weekend, Israel had violated the terms of their cease-fire and said the deal was in danger. Only 137 trucks with badly needed humanitarian aid made it through on Friday, the first day of the truce, and 187 on the second day, according to the U.N. Palestinian refugee agency. Israel had promised to permit 200 a day.

Qatari officials resorted to face鈥恡o鈥恌ace meetings with Israeli officials to try to save the deal, according to the diplomat. A few hours with Mossad officials in Tel Aviv proved crucial on Saturday. Suddenly, the deal was back on. Hamas handed over its second batch of Israeli hostages, families in the West Bank rejoiced over another 39 women and teenagers freed from prison, and Palestinians in Gaza emerged from their shelters to search for fuel and missing family members.

Qatar鈥檚 assistant foreign minister, Lolwah Al-Khater, became the first foreign official to visit the besieged Gaza Strip on Sunday. He used the pause in fighting to survey the disputed influx of aid, meet wounded Palestinians and talk with , Gaza bureau chief of Qatari-funded Al Jazeera, who lost his wife, son and grandchild in an Israeli airstrike. The pan-Arab broadcaster, which has more cameras in Gaza than any other news outlet, has dominated Arabic coverage of the war.

Despite their differences, both Israel and Hamas have an interest in prolonging calm. Even as bigger questions mount over what happens after the war, a Qatari official who spoke on condition of anonymity because of the sensitivity of ongoing negotiations says his country stays focused on what鈥檚 immediately possible, such as maintaining the cease-fire and preventing a regional war that draws in Hamas鈥� Iranian patrons or Lebanon鈥檚 Hezbollah militants.

A steady stream of officials have passed through Doha to that end, including Iran鈥檚 foreign minister, Lebanon鈥檚 caretaker prime minister and the director of the CIA.

鈥淭here is no conflict that began and ended on the battlefield,鈥� Majed al-Ansari, spokesperson for Qatar鈥檚 Foreign Ministry, told The Associated Press on Monday. 鈥淣ow, as hostages are being released and there are pauses in the fighting, we might be able to find a solution.鈥�

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