A 48-inch export pipeline was also shut on Monday after being attacked, but the damage was minor and the pipeline should be able to operate normally on Wednesday along with a smaller pipeline, the official said.
"We expect the situation to improve tomorrow and have both pipelines running," he said on condition of anonymity.
Two tankers were loading from the Basra offshore terminal, formerly known as al-Bakr Port, at a rate of 40,000 barrels an hour before flows through the smaller 42-inch pipeline stopped.
The attack on the 48-inch pipeline from southern oilfields to two offshore Arabian Gulf terminals came as oil prices hovered at record highs, partly driven by concerns that instability in Iraq would keep interrupting the country's exports.
The attack cut export flows to 1.1 million barrels a day from 1.9 million, the Iraqi official said.
Other oil officials on Monday had said output was halted in response to threats from fighters loyal to Shia Muslim leader Muqtada al-Sadr. An aide to al-Sadr has denied such threats were made.
Clashes between al-Sadr's supporters and US-led forces have spread to the deep south - a centre of Iraq's oil industry.
Iraq's South Oil Company asked its Basra headquarters employees not to come to work for the second day on Tuesday, but officials said there were enough staff at stations and oil platforms to keep exports flowing.
The two offshore terminals south of the city of Basra account for all of Iraq's exports. Attacks have kept another pipeline running to Turkey from the north mostly shut since the US-led invasion last year.