The strong exports point to Iran's success in regaining market share in Asia after the sanctions were eased in January, Reuters reported.
Before 2012, Iran exported around 2 mbd, with more than half going to Asia, mainly China, South Korea, India and Japan.
Tehran has been banned from selling oil to the United States for decades.
Iran's oil flows to Europe have also begun to pick up after a slow start.
Imports by Iran's top four buyers – China, India, Japan and South Korea – came to 1.56 mbd in March, up 49.9 percent from a year ago, government and tanker-tracking data shows.
India's imports last month totaled 506,100 bpd, the highest in five years, the data showed. The nation's imports from Iran are set to surge to a seven-year high during the fiscal year of 2016/17, industry sources said.
South Korea's imports in March fell slightly from a two-year high in February to 264,452 bpd but were still 94.5 percent higher than a year ago. Imports by China and Japan fell from a year ago.
Also, a Reuters survey found on Friday OPEC's oil output rose in April to close to the highest level in recent history, as production increases led by Iran and Iraq more than offset a strike in Kuwait and other outages. Iran is just trying to retrieve its pre-sanctions ceiling.
Top exporter Saudi Arabia, however, made no major change to output, the survey found, despite the kingdom hinting it could boost supply after OPEC and non-member nations failed to agree to freeze output at a meeting on April 17.
Oil LCOc1 has rebounded more than 75 percent from a 12-year low in January to reach $48 a barrel, helped by the freeze initiative and signs that lower prices are starting to curb higher-cost supply, despite high inventories and other persistent reminders of a glut.
Supply from the Organization of the Petroleum Exporting Countries rose to 32.64 million barrels per day (bpd) this month, from 32.47 million bpd in March, according to the survey, based on shipping data and information from sources at oil companies, OPEC and consultants.
That almost matches January's 32.65 mbd, when Indonesia's return as an OPEC member boosted production and output from the other 12 members was the highest in Reuters survey records, starting in 1997.
OPEC output has surged since it abandoned in 2014 its historic role of cutting supply to prop up prices, led by higher supply from Saudi Arabia and Iraq.
Iran saw the sharpest increase in production in April after Western sanctions were lifted in January. Tehran, which wants to recover the market share it lost, has refused to limit its supply until it reaches pre-sanctions output.
Iraq, which saw the fastest growth in production in OPEC in 2015, also raised output. Southern exports have risen to what may be a new record in April - depending on whether tankers loading at the end of the month are treated as April or May. Shipments of Kurdish crude from the north also rose.
OPEC's third-largest supply increase in April came from the United Arab Emirates, following the end of maintenance work on oilfields that produce Murban crude.
Of the countries that reduced output, the largest decline was in Kuwait due to a three-day workers' strike which temporarily more than halved oil output and curbed refinery operations.
Nigerian output fell due to the continued lack of Forcados crude exports and a brief disruption to shipments of another stream, Brass River. Repairs on a pipeline to the Forcados terminal will take until June, the government said.