He criticised the Sudanese government over the "completely unacceptable" situation in Darfur and accused it of breaking ceasefire agreements signed with rebels.
"I am committed to stepping up international efforts to bring a change of mind and action from the government of Sudan," he said.
Speaking on the eve of International Day for Darfur, Blair insisted that the crisis was "at the top" of his agenda as a number of human rights campaigners wrote an open letter to him in Britain's Independent newspaper.
"I have already talked to (Chinese) Premier Wen and President George Bush about Darfur in the last few days," he said.
"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 added 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," Mr Blair said.
His comments echo those by US President Bush that he was "frustrated" with the UN for failing to get a robust 20,000-strong force into the war-wracked province, again calling the situation in Darfur a "genocide".
Oscar-winning Hollywood star George Clooney and Nobel laureate Elie Wiesel pleaded with the Security Council to act, with the actor calling the situation "the first genocide of the 21st century".
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.