Palestinians walk past a tent amid the rubble in a destroyed area, amid a ceasefire between Israel and Hamas in Gaza, in Gaza City. REUTERS/Dawoud Abu Alkas

CAIRO (Reuters) -Gaza mediators -- the United States, Egypt and Qatar -- stepped up their efforts this week to stabilise the early stages of the truce between Israel and Hamas and to push forward U.S. President Donald Trump's 20-point ceasefire plan.

WHAT IS THE STATUS OF TALKS?

A Hamas delegation led by the group's exiled Gaza chief, Khalil Al-Hayya, has been in Cairo for talks with Egypt since Saturday.

U.S. Vice President JD Vance is in Israel on Tuesday after envoys Steven Witkoff and Jared Kushner met Israeli Prime Minister Benjamin Netanyahu on Monday. Egyptian officials have also met Netanyahu.

The first phase of the ceasefire involved stopping fighting, returning hostages, increasing aid flows and a partial pull-back of Israeli forces to a "yellow line".

WHAT HAS EACH SIDE DONE UNDER THE TRUCE?

Israel's forces have pulled back from some parts of Gaza, but around half of the strip remains under Israeli control. On Monday, the military said it began marking the withdrawal line, warning Hamas and residents to stay away.

Hamas has released all 20 living hostages it was holding and 13 bodies, leaving 15 deceased hostages still in Gaza. Hamas says rubble and other factors may complicate the retrieval of a number of bodies. Israel believes Hamas can quickly return around five more bodies and is stalling. An international task force is meant to locate the rest.

Israel has released around 2,000 Palestinians, including 250 long-serving inmates, but vetoed the release of some prominent militant leaders. It has returned 165 bodies of Palestinians to Gaza.

Israel has also facilitated the entry of more aid trucks through two crossings into Gaza, but UN and Palestinian officials said it remains far from sufficient.

WHAT PROBLEMS HAVE HIT THE TRUCE ALREADY?

There have been continued flashes of violence, particularly around the "yellow line" demarcating Israel's partial pullback inside Gaza.

Israel began marking out the line on Monday with yellow concrete blocks after repeated incidents of shootings. Israel says it has fired at suspected militants crossing the line. Gaza residents say it has not been clear where the line runs.

On Sunday, Palestinian militants killed two Israeli soldiers in Rafah. Israel responded with airstrikes that Gaza health authorities said killed 28 people. Hamas and Israel later recommitted to the truce.

Inside Gaza, Hamas has reimposed control, killing members of rival groups and those it accuses of collaborating with Israel. Trump signalled his endorsement of that but the U.S. military has said it must stop.

Hamas has said aid is flowing in too slowly. Israel says it is sticking to agreements.

The Rafah border crossing from Egypt to Gaza is also meant to reopen but has not yet done so.

WHAT'S BEING DISCUSSED FOR THE COMING PHASES?

A U.S.-backed stabilisation force is meant to ensure security in Gaza. Its composition, role, chain of command, legal status and other issues are yet to be agreed.

The United States has agreed to provide up to 200 troops to support the force without being deployed in Gaza itself. U.S. officials have said they are also speaking to Indonesia, the United Arab Emirates, Egypt, Qatar, Turkey and Azerbaijan to contribute.

Trump wants Hamas and other factions to disarm and Gaza to be demilitarised. The group has never accepted this and says mediators have not yet officially started discussing the issue with it.

Gaza is to be governed by a transitional committee of apolitical Palestinian technocrats. The composition of this body has not been agreed. Hamas has accepted the formation of this body, but says it would have a role in approving it.

The panel would be supervised by a new international transitional body called the "Board of Peace" headed by Trump. Its formation, and the possible inclusion of former British Prime Minister Tony Blair, is still to be agreed.

Hamas wants employees of the existing Gaza government it has run since 2007 to stay in their jobs. Israel says Hamas can have no role.

The phasing of further Israeli pull-backs is yet to be agreed, and will depend partly on Israel's own assessment of how much of a threat Hamas still poses. Hamas says the war will only end when Israel has fully withdrawn.

The Trump plan calls for the Palestinian Authority to be reformed. It is not clear what this would involve or what role it would take in future.

The plan says the truce could ultimately create the conditions for a credible pathway to Palestinian self-determination. Netanyahu has so far refused to accept the possibility of a Palestinian state.

(Reporting by Nidal al-Mughrabi and Maayan Lubell; Editing by Sharon Singleton)