In a television interview with America's CBS Evening News on Friday, Bush took a hard-line stance against the Hamas party, which swept Palestinian elections on Wednesday.
"If they don't, we won't deal with them," he said, speaking at the White House.
"The aid packages won't go forward. That's their decision to make, but we won't be providing help to a government that wants to destroy our ally and friend."
Earlier, the US State Department said all aid programmes to the Palestinians would be "reviewed".
"To be very clear, we do not provide money to terrorist
organisations," State Department spokesman Sean McCormack said on Friday.
Hamas, which has carried out scores of suicide bombings against Israeli targets, is classified by the United States as a terrorist group.
This year, the United States has budgeted no direct aid for the Palestinian Authority, although it plans to provide $150 million to the Palestinians through the US Agency for International Development, and another $84 million through the UN Relief and Works Agency for Palestinian refugees in the Near-East.
In addition to the threat of aid cuts, clashes between rival gangs have added to the problems facing the Palestinian territories after Hamas' shock victory in Wednesday's election.
"The aid packages won't go forward. That's their decision to make, but we won't be providing help to a government that wants to destroy our ally and friend"
George Bush, US President
As dusk fell over the Gaza Strip on Friday, thousands of Fatah supporters flooded the streets, demonstrating outside the parliament building in Gaza City to call for the resignation of Palestinian President Mahmoud Abbas and the rest of the Fatah party leadership.
In the southern Gaza Strip, violence involving Hamas and Fatah supporters in Khan Yunus and other nearby towns also highlighted lingering tensions.
Clashes there left at least nine people wounded, including five members of the security forces.
Monday's meeting of the quartet
will dicuss the next steps
International assistance will be a main topic when US Secretary of State Condoleezza Rice meets in London on Monday with foreign ministers from the European Union, Russia and the United Nations.
The four, known as the diplomatic "quartet", have been the main figures pushing the so-called "road map" to Middle East peace.
But Hamas' overwhelming victory against the long-dominant Fatah movement has thrown prospects for Middle East peacemaking into turmoil.
The victory also triggered alarm in Israel and across the world as the Hamas vow to destroy Israel is at odds with the road map's requirement that the Palestinians end violence against Israel.
Despite being behind the majority of attacks on Israeli targets during a five-year Palestinian uprising, Hamas has carried out no bombings for more than a year.
Yet international players in the stalled peace process made clear that Hamas would need to do more than hold fire if it wanted legitimacy.
The diplomatic "quartet" urged Hamas not only to renounce violence but also to accept Israel's right to exist.
The result has also confronted acting Israeli Prime Minister Ehud Olmert with his first major crisis since assuming the reins of power from coma-stricken Ariel Sharon on 4 January.
Olmert himself faces an election on March 28, aware his Kadima party's lead in the polls could be whittled away if the situation on the ground unravels.