Palestinians and Israelis have expressed cautious optimism that a deal on a ceasefire in the Gaza Strip and the release of hostages held there is close after 15 months of devastating war.

“I can’t believe that I am still alive to witness this moment,” 17-year-old Sanabel said in a voice note sent from Gaza City. “We’ve been waiting for this with bated breath since the first month of [last] year.”

Sharon Lifshitz, whose elderly father is among the remaining hostages, said: “I’m trying to breathe. I’m trying to be optimistic. I’m trying to imagine it’s possible that a deal will happen now and that all the hostages will return.”

Qatar’s foreign ministry spokesman said on Tuesday that there were no major issues blocking a deal between Israel and Hamas and that the indirect talks in Doha were focused on “the final details of reaching an agreement”.

An Israeli government official said the talks had made “real progress” and entered a critical and sensitive period, while Hamas said it was satisfied with the status of the negotiations.

US Secretary of State Antony Blinken said a deal was “right on the brink”.

Sanabel, who lives with her family in their partially destroyed home, told the BBC’s OS programme that everyone in northern Gaza was “feeling happy, cheerful, optimistic to see their best friends, to see their families who were displaced to the south of the Gaza Strip, to start over”.

The teenager said she had called her displaced best friend and discussed “what we would do if the war ended”, adding that she would start by trying to “make up for every moment that deprived me of seeing her”.

“But after I called her, there was a huge bomb in my area. This reminded me of the [last ceasefire and hostage release deal] in November 2023. There were huge bombs and missiles [before it started]. I’m really frightened that this will be repeated.”

“In the last hours of this war, I don’t want to lose one of my family members. I don’t want a ceasefire for a year or five months. I want a ceasefire for a long time – for the rest of our lives.”

Asmaa Tayeh, a young graduate who is sheltering with her family at her grandparents’ house in the western Gaza City neighbourhood of al-Nasr, also said people were once again daring to hope.

“You can never imagine how excited and nervous people are here,” she told the BBC. “Everyone is waiting as if they will only survive after the announcement.”

Asmaa is from Jabalia, Gaza’s largest urban refugee camp, whose residents have been forced to evacuate their homes multiple times by the Israeli military.

When the Israeli military launched a new ground offensive in Jabalia in October, Asmaa’s family was forced to flee once more.

Fierce fighting has raged in Jabalia ever since. In December, Asmaa said her whole area had been “wiped out”.

Relatives of Israeli hostages held in Gaza since October 2023 have also been speaking to the BBC about the news that a ceasefire deal could be imminent.

Sharon Lifshitz is a British-Israeli artist and filmmaker whose has had no news about her 84-year-old father Oded since the woman who was being held with him was released during the week-long ceasefire in November 2023.

“For us, we know there will be so much heartbreak. We know quite a few of [the hostages] are not alive anymore. We are desperate for the return first of the living ones so they can come back to their families. Each of them is a whole world,” she told the Today programme.

She said her mother, Yocheved – who was also abducted in the 7 October attack but was released weeks later – was sceptical about the chances of a deal but that “I can feel the cracks of optimism coming through”.

Eyal Kalderon – the cousin of 54-year-old Ofer Kalderon, two of whose children were among the 105 hostages released from captivity in November – said in a voice note sent to BBC OS: “We are hoping that the deal will be closed soon and we will reach the moment that we are hugging Ofer, that his four children are hugging him.”

“We want this deal to include all the hostages, all the 98 hostages. We are demanding that. We are just hoping to see all of them in Israeli [territory].”

Lee Siegel – the brother of Keith Siegel, 64, whose wife Aviva was also released in November – insisted: “All of the hostages must come home – those who are still alive, to work on rebuilding their lives and their families; those who are deceased, for a proper burial in their home country.”

Some families of hostages not included in the initial releases expressed anger that their relatives might be left behind if the deal falters at a later stage.

Ruby Chen’s son, Itay, was killed during the 7 October 2023 attack and his body is being held in Gaza.

“The prime minister unfortunately is moving ahead with a deal that does not include my son and 65 additional hostages, where it is not known how my son is going to come out. And for most of the families this deal is unacceptable,” he said.

Prime Minister Benjamin Netanyahu is facing opposition from far-right cabinet ministers and some in his own party, who object to prisoner releases and a wider ceasefire deal.

Sharon Lifshitz said a majority of Israelis had supported such a deal for a “very long time”, but that a combined pressure from the administrations of outgoing US President Joe Biden and President-elect Donald Trump had finally given Netanyahu’s government the “extra push” it needed.

“It appears that this deal is very much the deal that was on the table in July,” she added. “Many, many hostages died since July. Soldiers, Palestinians. So much suffering.”

Speaking later on Tuesday, Foreign Minister Gideon Saar said he was confident a majority in the Israeli government would support a deal.

Meanwhile Blinken – approaching the end of his tenure as US secretary of state – laid out for the first time the plan the Biden administration wants to hand over to Trump for post-war Gaza.

It did not envisage immediate full control of Gaza by the Palestinian Authority (PA) – the entity created by the Oslo accords that has limited governance in parts of the occupied West Bank.

Critically, Gaza’s security forces would be comprised of personnel from other countries – most likely Arab states although he didn’t name them – alongside “vetted” Palestinian forces.

Blinken said, as he has before, that Hamas had sought to spark a regional war and derail US-led efforts to integrate Israel and its Arab neighbours.

Meanwhile Israel, he said, had pursued its military campaign “past the point” of destroying Hamas’ military capacity and killing its leaders responsible for the 7 October attack.

He suggested this was self defeating, adding that the US assessed Hamas had recruited almost as many new militants as Israel had killed.

Israel launched a campaign to destroy Hamas in response to the group’s 7 October 2023 attack, in which about 1,200 people were killed and 251 others were taken hostage.

More than 46,640 people have been killed in Gaza since then, according to the territory’s Hamas-run health ministry. Most of the 2.3 million population has also been displaced, there is widespread destruction, and there are severe shortages of food, fuel, medicine and shelter due to an struggle to get aid to those in need.

Israel says 94 of the hostages are still being held by Hamas, of whom 34 are presumed dead. In addition, there are four Israelis who were abducted before the war, two of whom are dead.