According to the data, Essar Oil shipped in about 12.5 percent less oil from Iran in April from a year ago at about 156,600 bpd, Reuters reported.
India's Reliance Industries, owner of the world's biggest refining complex, imported 0.5 percent less oil in April from the previous month, the sources added.
The imports were, however, 17.3 percent more than a year ago, when the private refiner had slowed purchases ahead an annual maintenance at one of its plants, the data showed.
In the first four months of 2017, the private refiner shipped in 2.9 percent more oil from a year ago.
Iran has signed a flurry of deals with Western companies over the past year since the easing of international sanctions on Tehran following an accord over its nuclear program.
Iran needs foreign investment for repairs and upgrading of its oil and gas fields. It also seeks the transfer of technology to its oil industry after a decade of sanctions.
In November 2016, France's Total became the first oil major to sign a big deal with Tehran since the lifting of sanctions and agreed to help it develop the world's largest gas field, South Pars.
Shell signed a provisional deal in December to develop Iranian oil and gas fields South Azadegan, Yadavaran and Kish in December 2016.
Iran has named 29 companies from more than a dozen countries as being eligible to bid for oil and gas projects using the new, less restrictive contract model.
The firms include Shell, France's Total, Italy's Eni, Malaysia's Petronas and Russia's Gazprom and Lukoil, as well as companies from China, Austria, Japan and other countries.
Russia's Zarubezhneft signed an MoU for a feasibility study on two joint fields in the west of the country.
Norway's International Aker Solutions Company signed an MoU to modernize Iran's oil industry.
Last May, Austria's OMV signed an MoU for projects located in the Zagros area of western Iran and the Fars field in the south.
South Korean Daewoo Engineering and Construction (Daewoo E&C) signed an MoU to construct an oil refinery in Bandar Jask, on the southern coast of Iran.
Italy's Saipem signed MoUs to cooperate on pipeline projects, upgrading of refineries and development of Tous gas field in the northeastern province of Khorasan Razavi.
Norwegian oil and gas company DNO said it was the second Western energy company after Total to sign a deal with Iran under which it agreed to study the development of the Changuleh oilfield in western Iran.
Lukoil, Russia's second biggest oil producer, hopes to reach a decision on developing two new oilfields in Iran.
Germany's Siemens AG signed an MoU in May to overhaul equipment and facilities at Iran's oil operations and refineries.
BASF's Wintershall oil and gas exploration subsidiary signed an MoU with the National Iranian Oil Company in April 2016.