"President Bashir should take the last chance by responding to the secretary-general's efforts and to meet the just demands of the international community," Bush said, making clear he would not wait long.
Bush's warning comes just days after Sudan told the UN that it would accept a 3,000-strong UN force and equipment – including attack helicopters - to help the African Union force struggling to maintain security in Darfur.
Bush accused al-Bashir of routinely violating past agreements. Speaking separately to non-governmental organisations on Wednesday, Condoleezza Rice, the US secretary of state, also voiced scepticism that Sudan would honour agreements over Darfur.
"The fact of the matter is that we need to be prepared for the outcome that we have seen so often with the Sudanese, which is promises that are not met," she said.
Outlining the sanctions Sudan would face, Bush said the US treasury department would bar 29 companies owned or controlled by the Sudanese government from the US financial system, making it a crime for American companies to do business with them.
Washington would also impose sanctions on individuals responsible for violence.
He raised the possibility of an international no-fly zone aimed at preventing Sudan's military aircraft from flying over Darfur and accused the Sudanese of painting military planes white to disguise them as United Nations or African Union aircraft.
"I'm also looking at what steps the international community could take to deny Sudan's government the ability to fly its military aircraft over Darfur, and if we don't begin to see signs of good-faith commitments, we will hear calls for even sterner measures."
Bush said he would direct Rice to prepare a new UN Security Council resolution that would apply new sanctions against the government, imposing an expanded arms embargo and prohibiting it from conducting any offensive military flights over Darfur.
But he said "the situation doesn't have to come to that".
More than 200,000 people have been killed and 2.2 million forced to flee their homes in Darfur in nearly four years of fighting between the government and ethnic African rebels.