Mr Trump was speaking after a meeting with Israeli Prime Minister Benjamin Netanyahu at the World Economic Forum in Davos.
He said he aimed for peace in the Middle East and hoped sound minds would prevail among Palestinians to pursue peace.
But then he warned: “When they disrespected us a week ago by not allowing our great Vice President to see them, and we give them hundreds of millions of dollars in aid and support, tremendous numbers, numbers that nobody understands — that money is on the table and that money is not going to them unless they sit down and negotiate peace.”
The US President’s decision last year to recognise Jerusalem as Israel’s capital angered Arab nations and led Palestinians to refuse to negotiate with the US on grounds that America can no longer be an honest broker in the quest for peace.
Mr Netanyahu praised Mr Trump’s decision to recognise Jerusalem as Israel’s capital and to move the US Embassy there from Tel Aviv.
AHowever, a poll found Mr Trump’s decision had led to a spike in Palestinian support for “armed struggle”.
Nearly twice as many Palestinians said they supported “armed struggle” against Israel compared with an identical survey six months previously, while there was also a fall in support for the two-state solution, the joint Israeli and Palestinian poll found.
The poll of 1,270 Palestinians across east Jerusalem, the West Bank and Gaza was conducted in the days after Mr Trump’s December 6 declaration that he would move the US embassy from Tel Aviv to Jerusalem and recognise the city as Israel’s capital.
Khalil Shikaki, from the Palestinian Center for Policy and Survey Research and one of the report’s authors, said there had also been significant declines in Palestinian support for a peace process and compromise as well as in the popularity of Palestinian president Mahmud Abbas.
He said: “There is absolutely no doubt that the Trump statement was the fundamental cause.”
Dahlia Scheindlin from the Tami Steinmetz Center at Tel Aviv University, another report author, said she expected the support for militancy could fall in the coming months if tension subsides.
The US President arrived in Switzerland today to attend the World Economic Forum where he is set to push his “America First” agenda and seek more fair, reciprocal, trade between the United States and its allies.
Mr Trump, who was never invited as a businessman, is the first US president to attend Davos since Bill Clinton in 2000, giving him a chance to mingle with the same elite “globalists” he bashed in the 2016 election campaign.