The fight over the Beiji refinery, some 250 kilometres north of Baghdad, began Tuesday.
Col Ali al-Qureishi said the latest attempt by fighters came late yesterday. Al-Qureishi told The Associated Press today that he believed the militants were regrouping to launch a new attack.
There was no immediate way to independently verify al-Qureishi's claims.
Its loss would be a devastating symbol of the Baghdad government's powerlessness in the face of the offensive by Sunni militants of the Islamic State of Iraq and the Levant. The militants captured much of northern Iraq in a lightning offensive last week.