At a press conference in Havana, where Omar al-Bashir and Kofi Annan are attending the Non-Aligned Movement's summit, the Sudanese president said: "Justice is and remains our objective but through diplomatic, political and other means...that's why we reject this position."
Annan urged the government of Sudan to accept the UN Security Council's decision to replace the largely ineffective African Union force in Darfur with better-equipped UN peacekeepers.
He said: "There can be no military solution to the crisis in Darfur.
"All parties should have understood by now, after so much death and destruction that only a political agreement, in which all stakeholders are fully engaged, can bring real peace to the region."
The possibility of UN intervention was welcomed by Salva Kiir Mayardit, a Sudanese vice president with ties to the southern rebels who have been battling Janjaweed fighters.
The mandate for a weak African Union peacekeeping force, which hasn't been able to stop the violence, expires next month.
On Friday, George Bush, the US president, said it could be time to send international peacekeepers into Darfur despite the objections of the government in Khartoum.
Tony Blair echoed Bush's statement on Saturday: "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."
Blair's comments come ahead of a global day for Darfur planned for Sunday, when activists and religious leaders throughout the world will hold demonstrations and meetings to raise political awareness about the humanitarian crisis in the region.
A British official said that incentives could include ending suspension of development and recovery aid, resolving Sudan's debt situation, establishing higher level political contacts and moving towards the lifting of sanctions.
Jose Manuel Durao Barroso, the European Commission president, and Louis Michel, the commissioner for development, are to visit Sudan soon to step up the EU's engagement in the issue.
Antonio Guterres, the United Nations high commissioner for refugees, said international divisions had allowed the Sudanese government greater scope to manoeuvre.
Guterres told BBC radio: "The problem is the international community is not clearly united in a front to make sure that things really happen."