"This policy of threats ... will not work with the Palestinian people," spokesman for the Palestinian presidency, Nabil Abu Rudeineh, said in a press conference on Thursday.
"The issue of Jerusalem is a holy issue - it is the key to war and peace in the region. It cannot be bought or sold with all the world's money," said Abu Rudeineh, according to the official Palestinian news agency, Wafa.
"If Jerusalem is off the negotiating table, so is the US."
Trump threatened to withhold funds on Thursday after a meeting with Israeli Prime Minister Benjamin Netanyahu at the World Economic Forum in Davos, Switzerland.
"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," he said.
Trump did not specify which aid money he was referring to. Since 2008, the US has donated about $400m annually in economic aid to the Palestinian Authority - the governmental body that governs the Israeli-occupied West Bank.
Last week, the US decided to cut more than half of its funding to the United Nations agency for Palestinian refugees (UNRWA) - an aid agency that has been the lifeline to the more than five million registered Palestinian refugees in the occupied territories, as well as Lebanon, Jordan and Syria.
In Davos, Trump also accused the Palestinian leadership of "disrespecting" the US by refusing to meet Vice President Mike Pence during his visit to Israel and the region earlier this week.
Palestinian official Hanan Ashrawi responded by saying, "not meeting your oppressor is not a sign of disrespect, it is a sign of self-respect".
The developments come following a controversial decision by the US on December 6 to recognise Jerusalem as the capital of Israel. The US also vowed to move its embassy from the commercial capital, Tel Aviv, to Jerusalem.
The declaration dealt a blow to the Palestinian leadership, which for more than two decades has attempted to establish a Palestinian state on the territories occupied by Israel in 1967, consisting of the West Bank and Gaza, with East Jerusalem as its capital.
"We took Jerusalem off the table, so we don't have to talk about it anymore," Trump said on Thursday. "We'll see what happens with the peace process, but respect has to be shown to the US, or we're just not going any further."
Trump's Jerusalem decision also sparked anger across Palestine and the wider Arab and Muslim world and earned the US angry rebuke from the Palestinian President Mahmoud Abbas, who vowed not to receive Pence in the Palestinian territories.
During his speech in Jerusalem on Monday, Pence promised the American embassy would be relocated by the end of next year.
'Horror' over cuts to UN aid agency
Separately, a group of more than 20 celebrities and public figures - including actors Hugh Grant and Viggo Mortensen - condemned Trump's decision to cut funding to UNRWA.
On Thursday, the Hoping Foundation, a UK-based group that supports Palestinian children, released a joint statement expressing "horror" over the aid cuts.
"The real target of this lethal attack is the Palestinian people themselves. It has been launched with the clear aim of dismantling their rights, by dismantling the institution that is charged with protecting them," the statement said.
"2018 opens with President Trump's new attempt to force Palestinians to accept this grossly unfair 'deal', by threatening and endangering the international agency responsible for their basic needs as refugees.
"It is repellent to us that such tactics are being used in the 21st century, in direct contradiction of international law, and to human decency."
Actresses Emma Thompson and Olivia Wilde, as well as British author Hanif Kureishi, were also among the signatories.