Tony Blair said: "I am committed to stepping up international efforts to bring a change of mind and action from the government of Sudan."
He added that the international community could not "just watch as this tragedy deepens".
Speaking on the eve of Sunday's International Day for Darfur, Blair insisted that the crisis was "at the top" of his agenda.
"I have already talked to [Chinese] premier Wen and president George Bush about Darfur in the last few days.”
"In the coming weeks, I will talk to other leaders to agree an initiative that sets out the help Sudan can expect if the government lives up to its obligations and what will happen if they don't."
He also said that he "did not understand" Khartoum's rejection of the peacekeeping force authorised by a UN Security Council resolution last month.
"The government of Sudan must agree to the continuation of the African Union force and transition to the UN.”
Blair's comments echo those by Bush that he was "frustrated" with the UN for failing to get a 20,000-strong force into the war-wracked province, again calling the situation in Darfur a "genocide".
Darfur has been in the throes of a civil war since 2003 which has pitched rebel groups against the Khartoum government and allied Arab militia.
The conflict has killed around 300,000 people and displaced more than 2.5 million, according to the UN.
A peace accord signed in May between the Sudanese government and the main rebel groups was meant to end the conflict in the region but incidents between rebel factions in recent months have led to more deaths.