This was likely the first time the refiner is offering diesel with 10-parts per million (ppm) sulphur, from its usual sale of the less environmentally-friendly 500ppm sulphur diesel, traders said, though this could not be confirmed.
Essar Oil could not immediately be reached for comments.
The move follows an upgrade of a gasoil unit at its 400,000-barrel-per-day (bpd) Vadinar refinery in India's western Gujarat state in October, last year.
The company had converted its vacuum gasoil hydrotreater unit to mild hydrocracker unit, which allows for production of cleaner diesel.
In a bid to combat rising pollution in Asia's third-largest economy, the country will go straight to Euro 6 gasoline and diesel by 2020 from the current Euro 4 fuels in major cities and Euro 3 fuels across the rest of the country.
This means refiners will have to step up investments in upgrading their gasoline and diesel quality.
Currently, Reliance is the only refiner to export the 10ppm sulphur diesel from the country, which is mainly sold to Europe or Africa, traders said.
Essar Oil offered a 65,000-tonne cargo a month of either 10ppm sulphur diesel or 500ppm sulphur diesel for loading from Vadinar over April to September, a tender document showed.
Buyers also have the option of bidding for 38,000 tonnes of 500ppm sulphur gasoil and 40,000 tonnes of 10ppm sulphur diesel during April to September, according to the document.
The tender closes on January 14 and is valid until January 21.
© Thomson Reuters 2016