Sudan's government must start to "live up to its obligations" in the troubled Darfur region, Tony Blair has warned.
The prime minister called on Sudanese leaders to stop military action in the area and said he did not understand why they had rejected plans for a UN force.
As many as 200,000 people are thought to have died in three years of fighting and Mr Blair urged the world not to "just watch as this tragedy deepens".
An international day of events for Darfur is planned for Sunday.
Celebrities and religious leaders have called on the UK to take action.
In 2003, ethnic violence erupted between pro-government Arab militia and black Africans - who make up the majority of the region's population.
Since then, thousands of people have died and as many as two million have been displaced.
African Union (AU) soldiers have been policing the conflict, but they are due to leave at the end of September.
The UN intended to send a 20,000-strong peacekeeping force to replace the AU soldiers, but the Khartoum government has refused to accept the plan.
Mr Blair said he had thought the signing of the Darfur Peace Agreement in May by the government and one of the rebel groups would "set Darfur on the road to peace".
"The non-signatory rebel groups must now accept [the agreement] and the government of Sudan must stop its military campaign," he said.
Mr Blair described the coming weeks as being "crucial" for Sudan
"I do not understand the government of Sudan's rejection of the UN force, or its threat to withdraw its welcome from the AU."
Mr Blair pledged that Darfur would stay at the top of his agenda, adding he had already discussed the issue with US President George Bush and Chinese Premier Wen Jiabao.
"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."
International Development Secretary Hilary Benn said Sudan's leaders were "standing in the face of united world opinion".
"Above all, they're not doing the right thing by the people they seek to represent," he said.
Liberal Democrat leader Sir Menzies Campbell described the situation as the "true test of the resolution" of the international community.
"At long last the world is beginning to sit up and realise the enormity of what is taking place in Darfur," he said.
An open letter to Mr Blair signed by prominent figures including former Archbishop of Canterbury Lord Carey urged the government to "move Darfur to the top of its priority list".
Campaigner Bob Geldof, pop stars Annie Lennox and Elton John, and Body Shop founder Anita Roddick were among the celebrities who signed the letter.
Meanwhile, Muslim, Jewish and Christian leaders will gather outside Downing Street on Sunday to call for an end to the crisis as part of the International Day for Darfur.
Prayers written by Archbishop of Canterbury Dr Rowan Williams, Archbishop Desmond Tutu, Chief Rabbi Jonathan Sacks and Sheikh Ibrahim Mogra will be read from 1230 BST.
The Catholic Bishop of El Obeid, whose diocese includes Darfur, has also sent a message.
Events are planned in 30 capital cities around the world as part of the international day.
On Thursday, Oscar-winner George Clooney told the UN Security Council members that genocide was taking place "on their watch".
"It is the first genocide of the 21st Century and if it continues unchecked, it will not be the last," he said.