Jared Kushner, Donald Trump's son-in-law and Middle East envoy, has held lengthy talks with Israeli Prime Minister Benjamin Netanyahu, the premier's spokesperson has told the BBC, in a bid to restart the stalled US-backed Gaza peace plan.

Hailing the "very good meeting", Kushner told Fox News that there could be "progress in as little as 30 days, hopefully, on starting to take some of [Hamas's] weapons out," but added: "we do need cooperation from both sides".

Israel has said that it agrees with the Board of Peace, set up by the president, that there would be no reconstruction in Gaza without Hamas's complete disarmament.

Hamas had earlier asked the board to "compel" Israel to accept the peace plan, after Kushner held rare talks with the group on Sunday.

Trump leads the Board of Peace, which was created as an international organisation originally intended to bring peace to Gaza, but later expanded to include conflicts worldwide.

Last week Israel rejected Trump's 15-point Gaza peace plan.

The document calls for Israeli troops to withdraw and Gaza to be rebuilt under a new civilian Palestinian administration. But Netanyahu said that no military pull-out would happen until Hamas is "genuinely" disarmed.

Speaking to Fox New late on Monday, Kushner said his meeting with Netanyahu lasted almost four hours.

"I think there were some valid concerns that they raised that we were able to address," he said, adding that it would be a "win-win situation" for Israel if it accepted the peace plan.

When asked about his meeting with Hamas, Kushner replied: "They said all the right things - but obviously it's very, very hard to trust a terrorist organisation that committed these terrible atrocities.

"But we had a very cordial meeting... We [are] gonna give them a chance to perform."

According to Israeli media reports, Board of Peace envoys Nickolay Mladenov and Tony Blair also met Netanyahu on Monday.

In a statement after the meeting, the Israeli prime minister's office struck a diplomatic tone, saying Netanyahu and the board had "deep and constructive discussions".

It said they "agreed to establish two working groups, one on disarmament and demilitarisation of Gaza, which both Israel and the Board of Peace are determined should be prompt and completed before any reconstruction happens in Gaza".

It added that a second working group "will focus on sanitation, clean water and other public health issues for the people of Gaza and which also impact the people of Israel".

Many Israelis remain sceptical that Hamas is ready to disarm.