The Baiji refinery was shut down on Tuesday after rebels launched an attack.
Al Jazeera’s Omar al-Saleh, reporting from Baghdad, said while the Iraqi government said it was “in full control of that refinery”, the ISIL fighters still controlled the surrounding town.
“The fighters from the Islamic State of Iraq and the Levant withdrew from that installation, however they might attack at any time,” al-Saleh said.
A government spokesman said earlier on Thursday that Iraqi forces were in “complete control” of the site but a witness said the fighting was continuing.
Baiji lies in territory captured in the past week by the ISIL fighters and its Sunni allies, and is close to Tikrit.
The Iraqi government made a public request for US air strikes on Wednesday to thwart the assault.
The US has urged Maliki to reach out to Sunnis, many of whom feel excluded by the Shia parties that have dominated elections since Saddam Hussein was overthrown.
The secular Baath party, a political monopoly under Saddam, called on Iraqis to unite against Maliki.
“All the true, vibrant colours of our great Iraqi people must come together under one banner, against the American and Iranian conspiracies and their treacherous government under Maliki and their disgraceful sectarian and ethnic militias.”
Iraq’s neighbours have also urged political intervention as the only solution to heal the country’s sectarian divisions.