A senior Palestinian official involved in negotiations between Hamas and Israel said the talks had entered a "decisive and final phase".
Meanwhile Israel's defence minister, Israel Katz, said that a deal with the Palestinian terror group was closer than ever.
Speaking to the BBC, the Hamas negotiator outlined a three-phase plan, based on the deal US President Joe Biden outlined on May 31, which would see the release of some hostages and a ceasefire, reportedly for six to eight weeks.
It comes after an Israeli delegation flew to Doha on Monday to negotiate with mediators in the Qatari capital.
Hamas described the talks as “serious and positive”, and said a deal was possible if Israel stopped setting “new conditions”.
Senior officials from the US, Qatar and Egypt have resumed negotiation efforts in recent weeks and have reported a greater willingness from both sides to reach a deal.
A White House spokesperson said the warring parties were edging closer to a ceasefire.
Speaking in an interview with Fox News, John Kirby said: “We believe – and the Israelis have said this – that we're getting closer, and no doubt about it, we believe that, but we also are cautious in our optimism.
"We've been in this position before where we weren't able to get it over the finish line."
Following negotiations in Doha, Hamas said in a statement on Tuesday: “Hamas affirms that, in light of the serious and positive discussions taking place today in Doha under the auspices of our Qatari and Egyptian brothers, reaching an agreement for a ceasefire and a prisoner exchange is possible if the occupation ceases to impose new conditions.”
A Palestinian official said discussions were underway about every word in a ceasefire deal.
Speaking to the Israeli parliament's foreign affairs committee on Monday, Katz said: "We have not been this close to an agreement on the hostages since the previous deal," referring to the negotiated exchange of hostages and Palestinian prisoners in November 2023.
He has since written on X: "My position on Gaza is clear. After we defeat Hamas's military and governmental power in Gaza, Israel will have security control over Gaza with full freedom of action.
"We will not allow any terrorist activity against Israeli communities and Israeli citizens from Gaza. We will not allow a return to the reality of before 7 October."
CIA Director William Burns, an important US negotiator, was due in Doha on Wednesday for negotiations with Qatari Prime Minister Sheikh Mohammed bin Abdulrahman Al Thani on resolving remaining issues between Israel and Hamas, sources told Reuters.
Speaking to the BBC, the Palestinian official involved in indirect negotiations outlined a three-phase plan leading to the end of the war.
The deal would see civilians and female soliders held hostage in Gaza freed in the first 45 days, while Israeli military forces would retreat from city centres, the coastal road and the strategic strip of land along the border with Egypt.
Displaced Gazans would be able to return to the north of the Strip, while a second stage would see the remaining hostages freed and Israeli troops withdrawn, before the third stage bringing in the end of the war.
It is understood that Hamas has softened on its previous demand that Israeli troops must withdraw from the Strip before any hostages are released.
Contentious issues which have halted previous negotiations including the presence of Israel troops in the Philadelphi and Netzarim corridors appear to have been sidelined for now.
Hamas and Israel are expected to deliver their responses to the mediators’ latest proposal.
Donald Trump’s victory in the November US presidential election ramped up momentum for a ceasefire deal to be reached.
This month, he issued a warning to Hamas on Truth Social, saying there will be “hell to pay” unless the hostages in Gaza are released by January 20, the date of his inauguration.
The president-elect sent his incoming special envoy for hostage affairs, Adam Boehler, to meet with Netanyahu about a deal on Monday evening.
Israeli Prime Minister Benjamin Netanyahu's office rejected reports by Reuters that he was heading to Cairo for Gaza ceasefire talks.
Instead, a spokesperson for Prime Minister Netanyahu said that he visited a buffer zone in Syria on Monday, an area currently seized by Israeli forces.
The territory was taken by Israel following the collapse of Syria's Bashar al-Assad regime, and Netanyahu affirmed that troops would remain in the area “until another arrangement is found that will ensure Israel's security".