Ban Ki-Moon, the UN secretary-general, has said he believes new negotiations with Sudan may be necessary to allow other nations to contribute to the force.
Ali Sadik, a Sudanese Government spokesman, told Al Jazeera any move to bring in non-African troops would be resisted: "The African Union calls for the solving of African problems by Africans themselves.
"This is why we accepted the African Union participation and involvement in the Darfur problem."
"Genocide is a crime against humanity as a whole, not just against it's immediate targets. It therefore falls on the world at large to act."
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The full 26,000-strong force, that is to replace a poorly-equipped AU contingent, is not expected to be on the ground before mid-2008.
However Hassan al-Turabi, a Sudanese opposition leader and one of the leading critics of the government’s policy in Darfur, told Al Jazeera he would not oppose troops from outside Africa being deployed.
"I know the record of African forces in the Congo and in West Africa, I follow it closely of course and it's not good.
"The governments are not that democratic, the soldiers sometimes enjoy it here because they pay them a bit better, now they are inside the town, they are doing nothing actually.
"I don't mind leadership from other countries."
In their Times editorial, Brown and Sarkozy said British and French junior ministers would visit Sudan, including Darfur, as part of a diplomatic push to bring about a quick ceasefire.
They said that only "a ceasefire, a peacekeeping force, economic reconstruction and the threat of sanctions can bring a political solution to the region".
The pair vowed to "redouble our efforts to make further progress", noting that "the situation remains completely unacceptable".
They also called for a political settlement that would allow Darfur to participate in Sudanese national elections in 2009.
The UN has said that more than 200,000 people have died and more than two million have been displaced by four years of conflict in Darfur.