Mr Trump's comments suggest he is planning to pull Palestinian aid funding
The US may stop aid payments to Palestinians who are "no long willing to talk peace", President Trump said.
On Twitter, Mr Trump said the United States received "no appreciation or respect" in return for its aid.
He also said his controversial recognition of the contested city of Jerusalem as Israel's capital took the hugely divisive issue "off the table" for new peace talks.
Palestinians had said the move showed the US could not be a neutral broker.
The decision in December was also overwhelmingly condemned at the United Nations, where 128 countries voted against Mr Trump's fulfilment of a campaign promise.
What did President Trump say?
The US President was tweeting a follow-up to earlier comments about aid payments to Pakistan, in which he said the US has received only "lies and deceit" in exchange for billions of dollars in aid.
What have the Palestinians said to anger the US?
Jerusalem is one of the world's most contested sites.
Israel claims the whole of the city as its capital. The Palestinians want East Jerusalem, occupied by Israel in the 1967 Middle East war, to be the capital of a future Palestinian state.
Mr Trump, however, decided to formally recognise Jerusalem as Israel's capital, despite being warned it could cause unrest in the region.
He also said he would move the US embassy there from Tel Aviv, where all other nations have their consulates.
After the announcement, Palestinian President Mahmoud Abbas said he would no longer accept any proposals from Mr Trump's government.
"The United States has proven to be a dishonest mediator in the peace process," he said.
He also called Jerusalem the "eternal capital of the state of Palestine".
What kind of aid does the US send to Palestinians?
Mr Trump's tweets followed remarks from Nikki Haley, the US envoy to the United Nations, in which she said the US would stop contributing to the UN's relief agency for Palestinian refugees.
The agency runs education, health, and social programmes. The United States is its largest governmental donor, handing over almost $370m (£270m) in 2016.
Speaking at a news conference, Ms Haley said: "The President has basically said that he doesn't want to give any additional funding, or stop funding, until the Palestinians are agreeing to come back to the negotiation table."
The United Nations' overwhelming condemnation was "not helpful", Ms Haley said; Nikki Haley points to a reporter off-camera at a media briefing in the UN, New York City. Image copyright - GETTY IMAGES
She said the UN's vote to condemn Mr Trump's Jerusalem decision was "not helpful to the situation".
"The Palestinians now have to show their will that they want to come to the table. As of now, they're not coming to the table but they asked for aid.
"We're not giving the aid, we're going to make sure that they come to the table," she said.
The withdrawal of aid is likely to have a significant impact on the UN agency's work, as the US contributes almost 30% of its overall funding.
In 2016, the second-largest donor, the European Union, donated less than half as much as the US.
-- Courtesy of BBC News