Iran, which used to be OPEC's second biggest oil exporter, has been raising output since 2016 to recoup market share lost to regional rivals including Saudi Arabia and Iraq.
While many Asian nations continued to purchase oil from Iran during sanctions, Western nations halted imports, halving Iran's overall exports to as little as one million barrels per day (bpd).
Last month, Iran exported about 1.1 million bpd to Europe including Turkey, almost reaching pre-sanction levels and only slightly below the 1.2 million bpd supplied to Asia, the source told Reuters.
Iran's exports to Asia last month were the lowest since February 2016, Reuters' calculations showed.
Oil exports to Asia fell as South Korea and Japan stepped up oil condensate purchases and bought less oil, said the source, who asked not to be identified as the information is confidential.
"Iran's condensate parked in floating storage has almost been exhausted because of higher purchases by Japan and Korea," the source said.
Exports to Asia were also hit by India's decision to cut annual purchases from Iran by a fifth for the fiscal year to March 2018.
After the lifting of sanctions, Tehran added new clients such as Litasco and Lotos and won back customers such as Total (TOTF.PA), ENI (ENI.MI), Tupras (RDSa.L), Repsol (REP.MC), Cepsa CPF.GQ and Hellenic Petroleum (HEPr.AT).
OPEC member Iran was allowed a small production increase under a December deal to limit output.
Iran's overall May oil production totaled 3.9 million bpd, the source said.
Iran is currently producing about 200,000 bpd of West Karoun grade, which the nation blends with other Iranian heavy grades for export, he said.
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