The boost from Opec puts output further above its target of 30 million barrels per day (bpd), underlining the focus of top exporter Saudi Arabia and other key members on market share.
Opec supply rose in May to 31.22 million bpd from a revised 31.16 million bpd in April, according to the survey, based on shipping data and information from sources at oil companies, Opec and consultants.
The group meets on Friday and is not expected to alter policy as oil has risen to $65 a barrel from a low close to $45 in January and there are signs of slowing growth in the higher-cost supplies that have been eroding Opec's market share.
"Anything but a renewed confirmation of the production target at the forthcoming Opec meeting would be a major surprise," Commerzbank analyst Carsten Fritsch said.
"The rapid rise in US crude oil production has been stopped and the oil price has recovered considerably." If the total remains unrevised, May's supply would be Opec's highest since it pumped 31.53 million bpd in August 2012, based on Reuters surveys.
The biggest increase came from Angola, which exported 58 cargoes in May, more than originally planned in April, according to loading schedules.
Top exporter Saudi Arabia has not reduced output from April's record high of 10.30 million bpd, sources in the survey said, as it meets higher demand from export customers and in domestic power plants.
Of the countries with lower output, Libya posted a decline as more supply was disrupted by unrest, and production in Nigeria slipped because of pipeline leaks that prompted Royal Dutch Shell's local venture to declare force majeure on exports from the Forcados stream.
Iraqi exports, which have helped push OPEC output higher this year, look set to have fallen slightly short of April's record level, according to this survey.
Although Iraq increased its northern exports further following a deal between Baghdad and the Kurdistan Regional Government, flows declined from the south, which produces the bulk of Iraq's oil.
Further increases are expected in later months, said a source familiar with Iraq's exports.
"We should do better in the second part of the year to close the gap between planned and the current figures," he said.
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