Southern Iraqi exports in the first 21 days of March averaged about 3.36 million bpd, compared to 3.43 million bpd in February, shipping data followed by Reuters and independent tracking by an industry source showed.
The fall suggests there is still no sign of extra supplies reaching the market from Iraq even though oil prices rallied this year to $71 a barrel for the first time since 2014, supported by an OPEC-led agreement to cut output.
Iraq says it is committed to the OPEC deal.
"We are seeing lower volumes," the source who tracks Iraq's exports said.
Southern shipments have fallen as one of the single point loadings used to fill tankers was under maintenance for part of March because of a leak, a shipping agent said. Also, loadings have dropped at the small port of Khor al-Amaya.
Iraq had been boosting exports from its southern terminals, which handle the bulk of such trade, to offset a halt in shipments from its northern Kirkuk oilfields in October after Iraqi forces seized control of fields from Kurdish fighters.
Northern exports have averaged 270,000 bpd so far in March, compared with an estimated 340,000 bpd in February, according to shipping data and the industry source. That is far below levels of more than 500,000 bpd in some months of 2017.
Iraqi oil officials say there are no plans to resume oil flow through the Kurdish-owned pipeline, as no agreement has been reached yet.
Northern exports could rise if Iraq goes ahead with a plan to export Kirkuk oil by truck to Iran, but this has been delayed.
Based on loadings so far, total exports in March have averaged 3.63 million bpd, down from 3.77 million bpd in February, 3.81 million bpd in January and 3.84 million bpd in December, according to Iraqi figures and loading data. Southern shipments reached a record in December.
OPEC, Russia and other producers are cutting output by about 1.8 million bpd until the end of 2018 in an effort to get rid of a global crude glut and support prices.
Iraq complied less with the supply deal than its OPEC peers, such as Saudi Arabia and Kuwait, for much of 2017, but the drop in Kirkuk output boosted Iraqi and overall compliance.