Blair, speaking on the sidelines of an informal EU summit, said he had received strong support from his fellow EU leaders and that it was essential "over the next few weeks to bring this to a crunch point".
Earlier on his spokesman said Blair would be seeking "other ways to apply pressure" on Khartoum if necessary to accept a UN force in Darfur.
Blair, who said he had spoken to US President George W. Bush on the subject on Thursday, told journalists that "it is very important that we put maximum international pressure on the Sudanese government now to allow a proper peacekeeping force in, under the United Nations, to halt violent action and to try to and bring every one around to the peace agreement that has been signed".
An advisor to Sudanese President Beshir said on Thursday after a meeting with Washington's top envoy that Khartoum continued to reject the deployment of UN peacekeepers in war-torn Darfur.
"Our position has not changed," Ghazi Salaheddin told reporters after meeting Andrew Natsios, who was on a mission to Khartoum aimed at winning Sudanese approval for the deployment of UN peacekeepers to replace an African Union force.
In an escalation of the row on Friday, the Sudanese military declared UN special envoy Jan Pronk persona non grata, accusing him of "waging war against the armed forces," in the latest tensions between Khartoum and the international community.
The general command accused Pronk of "openly intruding in the armed forces' affair".
The UN Security Council passed a resolution on August 31 calling for up to 20,000 peacekeepers to be dispatched to Darfur, an area the size of France where the small ill-equipped AU contingent has failed to restore peace.
At least 200,000 people have died as a result of fighting, famine and disease, and more than two million fled their homes since ethnic minority rebels launched an uprising in Darfur in early 2003, drawing a scorched earth response from the Sudanese military and its Arab militia allies.
The British side did not specify what measures may be taken if Sudan continued to refuse a UN force.
"Privately I think they know what the consequences are," said Blair spokesman Tom Kelly.
Britain is also offering carrots to Sudan, in the form of improved relations and development aid, but the threat of punitive sanctions appeared to be looming and some diplomats believe that UN sanctions are on the cards.
President Bush last week ordered that all US economic sanctions against the Sudanese government be maintained, and added a ban on all oil and petrochemical transactions.
"We have got to be sure that over the next few weeks we bring this to a crunch point... otherwise the situation in Sudan will deteriorate and it is not an issue which is acceptable for the international community to avoid," Blair told reporters.
The AU itself has said it wants to be relieved by the United Nations and urged Khartoum to accept a UN deployment when its own mandate expires at the end of the year.

Copyright AFP (Agence France-Presse), 2006