US President Donald Trump has said the Gaza ceasefire talks are "going along very well", despite no breakthrough in the latest round of indirect negotiations between Israel and Hamas in Qatar.

Discussions are set to resume on Tuesday, though a Palestinian source familiar with the talks told the BBC they have not made any headway.

Trump spoke to reporters as he hosted Israeli Prime Minister Benjamin Netanyahu in Washington DC on Monday evening. Afterwards, a senior Israeli political official said the talks in Doha were still some way off from what Israel wanted to achieve.

Trump has recently stepped up pressure on Israel and Hamas to agree a deal, saying he believed it would be done this week.

As they met for dinner, Trump and Netanyahu were asked about Israeli and US proposals suggested earlier this year to permanently relocate Palestinians from Gaza.

Trump said he had co-operation for this from countries neighbouring Israel, while Netanyahu said he was working with the US on finding countries that will "give Palestinians a better future".

"If people want to stay, they can stay, but if they want to leave, they should be able to leave," Netanyahu said.

The proposals to force Palestinians out of Gaza has been met by condemnation from the UN, Arab leaders, human rights organisations, and Western governments.

Arab countries, led by Egypt, have suggested an alternative plan involving massive reconstruction in Gaza while Palestinians stay there in temporary housing units.

The UN has warned that the deportation or forcible transfer of an occupied territory's civilian population is strictly prohibited under international law and "tantamount to ethnic cleansing".

Netanyahu also appeared to again rule out any potential Palestinian statehood, saying that Israel will "always" keep security control over the Gaza Strip.

"Now, people will say: 'It's not a complete state, it's not a state.' We don't care," he said.

The concept of an independent Palestinian state alongside Israel is supported by the vast majority of the international community, and about three quarters of UN member states officially recognise the State of Palestine.

Meanwhile, Israel's defence minister told Israeli media that he had instructed the military to prepare a plan to move all 2 million Palestinians in Gaza into a camp in the south after screening them to ensure they were not Hamas operatives.

The plan has been described by one Israeli human rights lawyer as an "operational plan for a crime against humanity".

Trump has previously said he would be "very firm" with Netanyahu about ending the war.

But a Palestinian official familiar with the ceasefire talks told the BBC on Tuesday that the three rounds of indirect negotiations between Hamas and Israel since Sunday have yielded no progress.

"The negotiations haven't made any headway, not even an inch," the official said.

"The Israeli delegation simply came to listen and has no real mandate to negotiate."

The official expressed astonishment at recent media reports claiming significant progress, calling them "delusional" and "misleading".

Another Palestinian official told the BBC: "Hamas is beginning to question Israel's true intentions, accusing it of fostering a false sense of optimism in Doha without any real progress in the discussions."

Trump said Hamas "want to meet and they want to have that ceasefire".

According to Israeli Army Radio, the senior Israeli political official told reporters in Washington following the Netanyahu-Trump meeting: "I don't know if a deal will be signed in the coming week - it requires pressure and patience."

"We're about 80-90% of the way toward what we wanted in the previous negotiations."

Meanwhile, the Israel Defense Forces (IDF) said five of its soldiers had been killed in the northern Gaza Strip. Israeli media said it was caused by a roadside bomb in the area of Beit Hanoun.

A Hamas spokesman said its fighters had delivered a "blow" to the Israeli military in an operation in the area.

The Hamas-run ministry of health said on Tuesday afternoon that at least 52 Palestinians had been killed by Israel in Gaza over the past 24 hours.

The US-backed ceasefire proposal currently under discussion would reportedly see Hamas release 10 living hostages and the bodies of 18 dead hostages in five stages during a 60-day truce.

Israel would be required to release an unknown number of Palestinian prisoners and withdraw from parts of Gaza, where it now controls about two-thirds of the territory.

Netanyahu also told reporters he had nominated Trump for the Nobel Peace Prize, reportedly a long-held goal of the US president.

"He's forging peace as we speak, in one country, in one region after the other," Netanyahu said as he presented Trump with a letter he sent to the prize committee.

Netanyahu is visiting the White House for the third time since Trump returned to power nearly six months ago.

But the leaders are meeting for the first time since the US joined Israeli attacks on Iranian nuclear sites and then brokered a ceasefire between Israel and Iran.

There is a strong sense that the recent 12-day war has created more favourable circumstances to end the Gaza war.

Witkoff said on Monday that a US meeting with Iran would take place in the next week or so. Trump also said he would like to lift sanctions on the Islamic Republic at some point.

Additional reporting by Raffi Berg