That is close to the record of 3.37 million bpd exported in November as OPEC's second-largest producer resumes the supply growth that has added to downward pressure on global prices.
Iraq looked set to exceed that rate, with exports in the first 24 days of April averaging 3.43 million bpd, according to an industry source and loading data. It was not immediately clear why exports appeared to drop off last week.
Baghdad had given verbal support to an initiative by OPEC and outside producers to freeze output. But they failed to reach a deal at an April 17 meeting, and rising exports from Iraq as well as other nations including Russia underline the challenges to any further attempt at curbing supply.
The Baghdad government, which relies on oil for nearly all its revenue, sold crude at average price of $33.26 per barrel, reaping $3.343 billion, Jihad said.
April's figures are for exports by the central government, which is now only shipping crude from southern terminals, and not through a northern pipeline to Turkey, Jihad said. That pipeline is also used by the Kurdish Regional Government to independently export crude from fields it controls in the north.
Iraq was the fastest source of supply growth in OPEC last year and boosted production by more than 500,000 bpd, despite spending cuts by companies working at the southern fields and conflict with Islamic State.
Iraqi officials and oil analysts expect further growth in the country's exports this year, but at a slower rate than 2015.