The New York Times published an article on Friday saying that after the assassination of Hamas political leader Ismail Haniyeh in late July, Hamas officials told Qatari mediators that they had new demands for the already faltering cease-fire talks, according to an Arab and an American official.

The proposal alarmed the Qatari prime minister, who spent months urging Hamas to compromise. With the support of his staff, he rejected the idea in meetings and calls with the Palestinian militant group, and Hamas eventually abandoned the idea, the officials said.

“As cease-fire and hostage-release talks have faltered and stalled in recent months, Qatar has used its influence with Hamas to try to break the impasse, according to interviews with more than a dozen officials familiar with the negotiations, including regional and U.S. officials. Most of the officials spoke on condition of anonymity so they could share details of the closed-door discussions,” the paper says.

Since the war began, Qatar, along with Egypt, has emerged as a crucial mediator between Israel and Hamas, hosting marathon discussions with Palestinian representatives in the Qatari capital, Doha, and relaying messages from the Biden administration to Hamas. The Qataris have also worked with the Israelis, even though the two countries do not have formal diplomatic relations.

Qatar’s efforts have gained greater urgency as negotiations have reached a dead end. Hamas and Israel are still far from reaching an agreement — and the goals of the deal appear to be constantly shifting.

The newspaper quoted two American officials as saying that Hamas had added new demands in recent days for the release of the hostages, and demanded more details about the release of Palestinian prisoners in the opening phase of the agreement.

Officials hope Qatar can persuade the militant group to drop those demands again and even scale back its demand for the release of prisoners after six hostages were killed in Gaza.

There has also been a sustained effort to keep the talks on track, with four officials telling the newspaper that Qatar persuaded Hamas to return to the negotiating table after Israel invaded Rafah, in southern Gaza, on May 6. In the weeks that followed, Qatar pressured Hamas to accept the compromise language in the proposal.

More recently, Qatar has persuaded Hamas to remain engaged in the talks, even as the militant group has said it no longer wants to negotiate. While Hamas has publicly claimed it did not participate in the last two rounds of formal talks in Cairo and Doha, it has privately engaged in less formal discussions with Qatari and Egyptian officials about those meetings and offered feedback on specific points, according to an Arab official and two American officials.

“Qatar has been pressing both sides to commit to a deal and make tough decisions in the negotiations to reach that deal,” Majed al-Ansari, a spokesman for the Qatari foreign ministry, told the newspaper.

Qatar has maintained close ties with Hamas for more than a decade and has hosted its exiled political leaders since 2012. The former Qatari leader, Emir Hamad bin Khalifa Al Thani, became the first head of state to visit Gaza under Hamas. Qatar also funds Al Jazeera, which has amplified Hamas’s messages.

“Throughout the war, the Gulf emirate, which has a history of ties to Islamists, has sought to present itself as an international interlocutor capable of bridging the gaps between the warring parties. At the same time, Qatar hosts the largest American military base in the Middle East. The mediation efforts in Gaza have given the country another opportunity to prove to the United States that it can be a strategic ally in achieving important American foreign policy goals,” the newspaper said.

The newspaper quotes Dana Shell Smith, the US ambassador to Qatar from 2014 to 2017: “The Qataris always want to show that they can be a good partner and the ceasefire talks allow them to do that.”

“Qatar, which has a small military, relies on the United States to provide it with a security blanket,” Shell Smith said, noting that Gulf powers Saudi Arabia and the United Arab Emirates have sometimes taken hostile stances against their Qatari neighbors.

American officials have praised Qatar’s handling of the cease-fire negotiations, saying it has supported U.S. attempts to pressure Hamas at crucial moments. But the warmth between Hamas and Qatar has made some American officials hesitant, two American officials said.

Qatar’s goodwill toward Hamas stems in part from years of financial support for Gaza. Qatar has sent hundreds of millions of dollars to Gaza—with Israeli approval—for poor families, infrastructure projects, and public-sector salaries, though Israeli officials recently said they regretted the decision because it enabled Hamas to divert some of the money toward military operations.

Since the war began 11 months ago, Qatari Prime Minister Mohammed bin Abdulrahman Al Thani has devoted a great deal of his time to trying to broker a cease-fire, even at the expense of other government projects, according to three officials familiar with the talks. They said the prime minister has been meeting with Hamas representatives twice a day, the newspaper reported.

Last June, Qatar stepped in when ceasefire talks again appeared to be deadlocked.

Israel insisted that the next stage of negotiations focus on multiple issues, while Hamas wanted to limit it to a prisoner exchange.

“According to Hussam Badran, a senior Hamas official based in Qatar, Qatar, in cooperation with the United States, presented Hamas with three possible formulation options as a compromise language. He added that Hamas representatives chose one of them. Hamas agreed that the next stage would focus specifically on the issue of exchange, a formulation that left the door open to discussing some other possible issues,” according to the newspaper.

“We did it because we are keen on the ceasefire issue,” Badran said. “If there are some phrases that would make the negotiations easier and lead to the same result — the end of the war — we have no problem.”

Three officials familiar with the negotiations said Qatar had to push hard to get Hamas to agree to this settlement language.

Al-Ansari, the foreign ministry spokesman, said Qatar was exerting pressure by putting ideas on the table, setting deadlines for responses and reminding both sides of the seriousness of the situation. “Qatar is able to engage with Hamas in a serious and open way because of its long-standing relationship with it and its support for Gaza,” Tamer Qarmout, a professor of public policy at the Doha Institute for Graduate Studies, told the newspaper. “Hamas understands that if the Qataris are pressuring it, it needs to engage with them and respond positively.”

Qatar's influence has its limits, as both Israel and Hamas take seemingly irreconcilable positions.

Besides the prisoner swap, negotiations have stalled in part over the fate of the Philadelphi Corridor, a narrow strip of land in Gaza along the border with Egypt. Israeli Prime Minister Benjamin Netanyahu has insisted that the Israeli military must remain in the corridor, while Hamas has said any deal requires Israel to withdraw from Gaza, including that border area.

Several officials familiar with the negotiations expressed concern that Netanyahu in recent weeks has put forward new demands that could delay or even torpedo the agreement, including keeping Israeli forces in the corridor.

Hamas also set up roadblocks throughout the operation.

In a meeting this summer with Hamas officials, Qatari mediators pressured the Palestinian militant group to agree to a version of a cease-fire agreement with Israel that was on the table.

Hamas officials responded that even if they were willing to do so, they could not give the green light without the approval of the group’s leadership inside Gaza, especially Yahya Sinwar, the region’s most powerful figure. The Qataris conceded that point, and the meeting ended without any progress, according to several officials familiar with the talks. “Those on the ground have the final say,” Mr. Qarmout said.