Speaking ahead of talks with Israel's prime minister on the sidelines of the economic summit in Davos, Trump said Palestinians had disrespected the United States by not agreeing to meet with Vice President Mike Pence during his trip to the region last week.
And he declared Jerusalem "off the table" in negotiations after he declared the disputed city the capital of Israel last year.
"They're going to have to want to make peace," Trump said, "or we're going to have nothing to do with them any longer."
"We'll see what happens with the peace process but respect has to be shown to the US or we'll just not going any further," he said.
The President's remarks sparked renewed debate about whether the US is still able to play the role of mediator in the decades-long Israeli-Palestinian dispute.
And flatly contradictory comments by Trump and some of his senior officials on the status of Jerusalem are raising questions about the administration's peace plan, which remains a mystery to most of the players on both sides.
The President's comments amount to an escalation in tone toward the Palestinians, with whom he must work if he hopes to strike an elusive peace accord. Instead of drawing them to the negotiating table with offers, he has scaled up his threats of what will happen if they don't agree to talks.
Trump already drastically reduced US aid last week to a United Nations fund that provides assistance to Palestinian refugees, sending just $60 million of a pledged $125 million.
Analysts have said the fund -- which provides emergency relief, health care and education for 5 million Palestinians in the West Bank, Gaza and neighboring countries -- has helped quell further violence in the region. Trump questioned the value of the investment.
"We give them tremendous amounts, hundreds of millions of dollars. That money is on the table, because why should we do that as a country if they're doing nothing for us?" he said in Davos. "And what we want to do is help them. We want to create peace and save lives. And we'll see what happens. We'll see what happens. But the money is on the table."
Palestinian officials reacted to Trump defiantly Thursday, arguing that the US has abandoned its role as an "honest broker."
"If Jerusalem is off the table, then America is off the table as well," President Mahmoud Abbas' official spokesman Nabil Abu Rudeineh said in a phone call with CNN, reiterating that Palestinians no longer recognize the US as a mediator in any peace negotiations with Israel.
There will be no negotiations, Abu Rudeineh said, until the current American administration abides by international law and agrees to work toward a two-state solution, which would see a state of Palestine created along 1967 lines with East Jerusalem as its capital.
Jordan's King Abdullah insisted the US continues to have a role to play.
Speaking at the World Economic Forum in Davos with CNN's Fareed Zakaria, Abdullah said Thursday that, "we cannot have a peace process or a political solution without the role of the US," but he also asked, "How do we bring everybody together?"
Jordan has a substantial Palestinian population, the King is custodian of the holy Muslim sites in Jerusalem and his country is deeply dependent on American aid.
Israeli Prime Minister Benjamin Netanyahu, also in conversation with Zakaria, insisted there is "no substitute for the United States as honest broker" in the peace process.
He added that it was "fantasy" for any other body to play this role. "If you want to enjoy the services of a great power, that can summon economic resources and political support for a potential peace, there is no one else other than the US," he added.
Asked if Trump aide and son-in-law Jared Kushner can make peace in the Middle East, Netanyahu said Trump has "a very able team" with "many abilities."
'A great proposal'
"The thing people don't realize is these people have made their mark in markets in real estate," Netanyahu said, before going on to stress that the central issue isn't land -- the position Palestinians take -- but recognition of Israel.
"This is not a real estate deal, fundamentally not a real estate deal, but a problem of recognizing Israel's existence," Netanyahu said, "a problem of not recognizing a Jewish state in any boundary, but also has real estate elements and they're -- I have to say -- very creative. I wait to see what they put down, but I don't rule it out."
Yet Thursday also brought renewed questions about the administration's larger vision for Mideast peace.
Trump refused to lay out a timetable for a US-brokered peace plan, but did say his administration has a "proposal for peace."
"It's a great proposal for the Palestinians; I think it's a great proposal for Israel," he said.
In New York, the US ambassador to the UN, Nikki Haley, gave a speech that hinted the timetable for talks might not be anytime soon and contained a clear ultimatum. Blaming the moribund state of peace talks entirely on Abbas, Haley hinted that unless he radically changes his approach, the US isn't interested in engaging with Palestinians as long as he remains their leader.
The US "remains deeply committed to helping the Israelis and Palestinians reach a historic peace agreement that brings a better future to both peoples," Haley told the Security Council on Thursday. "But we will not chase after a Palestinian leadership that lacks what's needed to achieve peace. To get historic results, we need courageous leaders."
Haley's speech also highlighted the disjointed nature of the administration's public remarks about its peace plan. While Haley said that, "we have done nothing to prejudge the final borders of Jerusalem," the President, in Switzerland, said that, "we have taken Jerusalem off the table."
The decision to recognize Jerusalem as Israel's capital was condemned by 128 countries in a UN General Assembly vote in December. Previous US administrations hewed to the international consensus that East Jerusalem, which includes the Old City and its key religious sites, would be the capital of any Palestinian state, subject to final status negotiations between Israelis and Palestinians.
Trump said in Davos that his decision to move the US Embassy from Tel Aviv to Jerusalem will be expedited, with a smaller embassy opening its doors next year. And he said that instead of forestalling peace talks, his Jerusalem decision makes the situation easier by eliminating it as a sticking point.
"I didn't set it back, I helped it just by taking it off the table. That was the toughest issue," he said. "And Israel will have to pay for that. Look, Israel, something's going to happen, they'll do something that's going to be a very good thing. But they want to make peace, and I hope the Palestinians want to make peace, and if they do, everybody's going to be very happy in the end."
Palestinians thought otherwise. Trump is "blackmailing the Palestinian people and punishing them for fighting and believing in their freedom and human rights," according to a statement from Palestine Liberation Organization Secretary-General Saeb Erekat, responding to Trump's remarks at Davos.
In New York, the Palestinian representative to the UN, Riyad Mansour, recalled the early days of the Trump administration, when there was some hope the President's interest in making "the ultimate deal" would spur progress.
"In the span of a year we have seen hopes rise for peace and the sudden dashing of those hopes," Mansour told the Security Council. "The dramatic deterioration of the situation, the escalation of tensions and the deepening of political deadlock are cause for great concern."