US President Donald Trump has promised to revive the stalled Israel-Palestine peace process after hosting Palestinian leader Mahmoud Abbas, without, however, offering any details about how to resolve the long-running conflict.

Speaking after their first face-to-face meeting at the White House on Wednesday, Trump pledged to support Abbas "in being the Palestinian leader who signs his name to the final and the most important peace agreement that brings safety, stability, prosperity to both peoples and to the region".

He also said he believes Israelis and Palestinians are both willing to make a deal.

"I've always heard that perhaps the toughest deal to make is the deal between the Israelis and the Palestinians," Trump said.

"Let's see if we can prove them wrong," he added. "We will get it done."

Al Jazeera's James Bays, reporting from the White House, said the meeting did not bring any clarity to the US policy on the Israeli-Palestinian conflict.

"We know what they want, but we don't know how they are going to get there," he said. "Trump is not telling us how he is intending to achieve the peace he is promising."

On his part, Abbas reiterated the Palestinian demand for an independent Palestinian state along pre-1967 lines, with East Jerusalem as its capital.

"Our strategic and sole option is to achieve the two-state solution, the state of Palestine with East Jerusalem as its capital to live side by side in peace, safety and stability together with the state of Israel along 1967 borders," he said.

MARWAN BISHARA, AL JAZEERA'S SENIOR POLITICAL ANALYST: Trump has basically said nothing of importance about the issue, other than promising that he wants to and he will resolve it while providing absolutely zero details about it. We have absolutely no idea how he plans to accomplish it and whether this is a series of false promises. This process started in 1993 and until today it has really remained stuck in some of the basic differences between the Israelis and the Palestinians that don't look like they can be bridged by anyone because of the imbalance of power, and because the gap has in fact widened between the two sides. What is quite surprising, and sad, is when Abbas said we rely on God and Trump - if that’s the Palestinians' last card today, the way to salvation and independence is to rely on God and Trump, then they are in trouble. Abbas has been president for 12 years, and elected only once. He really doesn't have much legitimacy among Palestinians today because he has been able to accomplish little other than symbolic gestures by the international community. On the ground, with the settlements increasing and thousands in prison, the situation continues to get worse.

"We are the only people in the world who remain occupied. That is why we are seeking our freedom, our dignity and the right of self-determination."

Abbas also told Trump that the Palestinians had hope in him.

"We rely totally on God Almighty, then on you and we promise to be true partners to achieve a historic peace agreement," he said.

Trump said that any agreement cannot be imposed by the United States.

"The Palestinians and Israelis must work together to reach an agreement that allows both peoples to live, worship and thrive and prosper in peace," he said.

Prisoners on hunger strike

While Abbas was meeting with Trump, thousands of demonstrators took to the streets across the West Bank, rallying in support of more than 1,000 Palestinian prisoners who have been on hunger strike for 17 days in Israeli jails.

The prisoners are demanding better conditions, including more family visits, improved medical care and an end to solitary confinement and administrative detention.

Al Jazeera's Harry Fawcett, reporting from Ramallah, said: "Lawyers who have filed a motion within the Israeli Supreme Court on behalf of the Palestinian prisoners said that they have come to some arrangement with the Israeli side to gain access to the hunger-striking prisoners which has been banned up until this point."

He said the ban was the part of the sanctions the Israeli prison system was taking against the hunger strikers for violating the code of behaviour by refusing to eat.

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Abbas made the trip to Washington while politically unpopular back home, with polls suggesting most Palestinians want the 82-year-old to resign.

He is hoping Trump can pressure Israel into concessions he believes are necessary to salvage a two-state solution to the conflict - the idea of Israel and Palestine living side-by-side and at peace has been the bedrock of US diplomacy for the past two decades.

But Trump, who promised during his election campaign to move the US embassy from Tel Aviv to Jerusalem, has previously challenged the legitimacy of Palestinian demands for a state and dropped his country's commitment to a two-state solution.

"Trump has in the past said he doesn't mind if it's a two-state or one-state solution," Al Jazeera's Bays said. "All we have in the place of the roadmap we had in the past is optimism from the US president."

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Abbas and Trump spoke by phone on March 11, and there are suggestions the US president could visit the Middle East this month.

Though expectations are low, plans are being firmed up for Trump to visit Israeli Prime Minister Benjamin Netanyahu in Jerusalem and possibly Abbas in the West Bank, on May 22-23, according to people familiar with the matter.

US and Israeli officials have declined to confirm the visit.

Mutual distrust between Palestinians and Israelis will be a formidable, if not impossible, barrier for Trump to overcome.

Trump faces deep scepticism at home and abroad over his chances for a breakthrough.

National Security Adviser H R McMaster said on Tuesday night that Trump "does not have time to debate over doctrine", and instead seeks to challenge failed policies of the past with a businessman's results-oriented approach.