An official quoted by Reuters said the militants now controlled 75% of the Baiji refinery, 130 miles north of Baghdad.
Government forces have made new air strikes on militants advancing towards the capital.
Fighting is also reported in the western city of Ramadi.
The government is battling to push back ISIS (Islamic State in Iraq and the Levant) and its Sunni Muslim allies in Diyala and Salahuddin provinces, after the militants overran the second city, Mosul, last week.
PM Nouri al-Maliki appeared on television with Sunni Muslim and Kurdish leaders on Tuesday to issue a call for national unity in the face of the advance – they demanded that non-state forces lay down their arms.
However, such a call is unlikely to have much effect as Nouri al-Maliki has openly sponsored the formation of Shia Muslim militias to fight alongside regular Iraqi troops.
Hundreds of people have been killed since the start of the militant offensive last week, many of them believed to be captured soldiers publicly shot by ISIS-led firing squads.
During fighting in the city of Baquba this week, 44 prisoners were killed inside a police station in unclear circumstances.
The attack on the refinery started at 04:00 a.m. from outside two of the three main entrances to the refinery, according to Reuters.
Smoke rose from a spare parts warehouse and some stores of oil were reportedly destroyed.
“The militants have managed to break into the refinery,” the unnamed official told Reuters from inside the refinery.
“Now they are in control of the production units, administration building and four watch towers. This is 75% of the refinery.”
Foreign personnel were evacuated earlier but local staff reportedly remained in place, with the military defending the facility.
Baiji accounts for a little more than a quarter of the country’s entire refining capacity, all of which goes toward domestic consumption for things like petrol, cooking oil and fuel for power stations, an official told AP news agency.
Militants in the western province of Anbar, where the capital is Ramadi, said they had made advances, with a number of police stations near the town of Hit going over to dissident tribes.
Further north, the Iraqi government said it had recaptured the citadel in the strategic town of Tal Afar, where militants were said to have taken control on Monday.
Using unusually strong language, Nouri al-Maliki accused Saudi Arabia – which is largely Sunni – of backing ISIS. He also fired four army commanders for failing to halt the sweeping advance by the militants. They included the top commander for Nineveh, the first province where ISIS fighters made major gains.
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