John Negroponte, second in command at the US state department, on an African tour, reinforced the message by urging Muammar Gaddafi, the Libyan president, to back the deployment of international peacekeepers in Darfur and on the Chad/Central African Republic border.
Sudan agreed on Monday to an interim support package in which 3,000 UN personnel and heavy support equipment would reinforce AU peacekeepers in Darfur, but have refused to accept the larger "hybrid" UN force, of 10,000 more troops, that the Western powers say are needed.
The 5,000 AU peacekeepers have been unable to stem the violence in Darfur, a territory as big as France, where at least 200,000 people have been killed and 2.5 million made homeless since 2003 in ethnic and political conflict triggered by a rebellion.
The violence has spilled over to Chad and Central African Republic.
Lam Akol, the Sudanese foreign minister, said earlier in an interview in Dubai that the US and Britain should help secure UN funds for the AU peacekeepers already on the ground instead of pushing for a larger UN force.
Bush warned Sudan's president that he had one "last chance" before the US imposes sanctions and considers other punitive actions.
But Bush also said he had decided to give Ban Ki-moon, the UN secretary-general, more time to pursue diplomacy with Omar Hassan al-Bashir, the Sudanese president.
He said al-Bashir must allow deployment of a full joint UN-African Union peacekeeping force to Darfur, end support for Janjawid militias, reach out to rebel leaders and allow humanitarian aid to reach the people of Darfur.
"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 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.
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.
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".
Mustafa Othman Ismail, adviser to the Sudanese president, told Al Jazeera that his country doubted the intention of the UN Security Council to impose more sanctions on Khartoum.
"All these statements by the British prime minister are not new," he said.
"The US strategy is to keep the situation in Darfur as it is in order to pressurise the Sudanese government to bow to their demands."
"The Abuja agreement, that was approved by the UN Security Council and backed by Britain and the US, clearly stated that the African troops are responsible for maintaining security in Darfur, not the UN troops."
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.