Iran exported in July 2.2 million barrels of oil per day to Asian and European markets, it said, with exports to Asia up by 100,000 barrels per day, Reuters reported.
China, South Korea, India and Japan are Iran's main crude oil buyers in Asia.
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.
India's imports of Iranian crude rose more than 30 percent in the first three months of the Indian financial year in April-June.
India's State Minister for Petroleum and Natural Gas Dharmendra Pradhan however has said India's state refiners will buy less Iranian oil in the upcoming months compared to the last fiscal year.
New Delhi wants Tehran to grant special rights to the development of a major gas field in the Persian Gulf to the Indians and its latest decision is apparently a response to Iran's refusal to submit to the demand.
Iran's Oil Minister Bijan Namdar Zanganeh has said India's purchase of less Iranian oil is a non-issue since his country has enough customers elsewhere.
According Iran's leading oil tanker operator NITC, shipments to Europe are increasing daily and the company plans to expand its fleet to cope with the situation.
The rise in July came after imports of Iranian crude by Asian buyers fell for a second month in a row to a 14-month low in June because of lower purchases by China and Japan.
China, India, South Korea and Japan together imported 1.46 mbd of Iranian crude in June, down 15.2 percent on a year ago and the lowest amount since 1.32 mbd in April last year, Reuters reported, quoting government and ship-tracking data.
Iran has been ramping up oil production since the removal of sanctions, aiming to hit pre-sanction levels of around 4 mbd by the end of the year from around 3.8 mbd in recent months.
The country has persuaded OPEC to exclude it from a deal under which members are bound to reduce their output by 1.2 mbd.
Nevertheless, a Reuters study released on Monday showed that OPEC oil output rose by 90,000 bpd in July.
Compared with the levels from which they agreed to cut, the 11 members have reduced output by 978,000 bpd of the pledged 1.164 mbd, the news agency said. That equates to 84 percent compliance, from a downwardly revised 77 percent in June, it added.