Israel and Hamas negotiators have exchanged lists of prisoners and hostages who would be released under the terms of any peace deal.
In a statement raising hopes of an imminent breakthrough in talks a statement signed by senior Hamas official Taher al Nunu also expressed optimism about reaching an agreement.
Negotiations currently taking place in Sharm El Sheikh, Egypt, are focussed on the "mechanisms for implementing the end of the war, the withdrawal of the occupation forces from the Gaza Strip, and the exchange of prisoners".
The release of 48 Hamas-held hostages - 20 of whom are thought to be dead - and 1,950 Palestinian prisoners are critical parts of US President Donald Trump's 20-point pathway to peace plan.
He wanted an agreement reached by the end of the week but the implementation of the first phase has not yet been agreed.
Before indirect talks started President Trump urged “everyone to MOVE FAST" before stating on his Truth Social media platform: "I am told the first phase should be completed this week."
The Palestinian militant group - responsible for the October 7 atrocity in 2023 that left 1,200 Israelis dead - has agreed to some but not all of his 20-point plan.
But the breakthrough is the closest both sides have come to a deal.
Part of the plan includes "creating the field conditions" for the possible release of all Israeli hostages in return for a number of Palestinian prisoners.
Hamas, which rules the Gaza Strip after seizing control in 2007, has agreed to some of the proposals but as yet failed to commit to full disarmament.
German Foreign Minister Johann Wadephul said the first phase of the US plan to end the war in Gaza must be achieved by the start of next week.
He said: “We now have the first phase of this US plan, and this first phase aims at a ceasefire, the release of hostages and also the release of Palestinian prisoners, restraint in the military conflict and, above all, that food, water, medicines and the most essential supplies are finally brought to the population in the Gaza Strip. We must now achieve this first phase this week, or at the latest by the beginning of next week.”
