The move by Opec in a monthly report follows a similar downward revision to oil demand growth in 2013 by the US Energy Information Administration on Tuesday.
Opec now expects world oil demand will rise by 800,000 barrels per day (bpd) this year, a cut of 40,000 bpd from the previous estimate. It cited weaker-than-expected oil use in developed economies, particularly Europe and Japan.
"Monthly data that is starting to emerge for the first quarter of 2013 suggests that OECD demand may be disappointing compared with our previous assessment," said the report by economists at Opec's Vienna headquarters.
Opec, the source of more than a third of the world's oil, has been flagging the prospect that demand may prove weaker than expected due to the euro zone's economic problems and uncertainties about the outlook for the US economy.
The EIA on Tuesday also cut its 2013 world oil demand growth forecast by 50,000 bpd, although it still sees a stronger rate of growth in oil demand than Opec of 960,000 bpd.
The third closely watched oil forecaster, the International Energy Agency, updates its outlook on Thursday.
In the report, Opec slightly increased the forecast demand for its own crude in 2013 by 40,000 bpd to 29.75 million bpd, due to a lower expectation of supplies from outside the 12-member group.
Opec's production is still running higher than that, although supply has been falling in recent months and, according to the report, declined again in March.
Output from the Opec members fell by 100,000 bpd last month to 30.19 million bpd, according to secondary sources cited by the report, led by Iran and Nigeria. That would be the lowest since March 2011, based on Reuters data.
That suggests Opec is pumping a mere 190,000 bpd more than its output target of 30 million bpd, which the group is scheduled to review at a May 31 meeting. Opec is not currently expected to make major changes to policy at the meeting.
Opec's report also indicated its top crude exporter Saudi Arabia is still keeping output flat after a sharp reduction in supply at the end of 2012, that coincided with a rise in oil prices.
Saudi Arabia told Opec it pumped 9.14 million bpd in March, steady from 9.15 million bpd in February.