Triesman said continuing attacks by some rebel groups in Darfur and the bad behavior of countries backing them did not excuse the Sudanese government from observing a cease-fire.
He said al-Bashir must implement a three-phase UN package it agreed to in November to help end the escalating violence in Darfur.
Sudan, he said, "has not observed the cease-fire, has committed military forces to try to achieve military solutions, has not disarmed any of the (pro-government) janjaweed (militia), and has not really engaged in a political process as contrasted with a military process."
The result, he said, was that conditions on the ground are getting worse and worse, while humanitarian organizations are finding it more difficult to get aid "to destitute, starving, dying people".
The 7,000-strong African Union force on the ground in Darfur was powerless to intervene, he said.
The UN package is supposed to culminate with the deployment of a 22,000-strong "hybrid" force of African Union and UN peacekeepers.
But in January al-Bashir said UN troops were not required in Darfur because the African Union force on the ground could maintain order.
Triesman said that Ban Ki-moon, the UN secretary general, was still awaiting an official reply from al-Bashir to his January 24 letter outlining the UN's positions on the hybrid force, command and control, and funding.
"It will be an important indication of whether he is in tune with the international community whether he responds urgently," he said.
The Darfur conflict began when rebels from ethnic African tribes rose up against the central government.
Khartoum is accused of having responded with indiscriminate killings by unleashing the janjaweed militias of Arab nomads - blamed for the worst atrocities in Darfur.
The government denies these charges.