LONDON -(MarketWatch)- Iran has stopped shipping oil to Greece and may halt supplies to Royal Dutch Shell PLC (RDSB.LN) over unpaid bills, Iran media said Friday, as the impact of sanctions widens.

The news suggests a decline in Iranian oil exports last month may accelerate as banking sanctions add to an upcoming European ban on Tehran oil. That could lead to upward pressure on oil prices, which have recently surged to a four-year high.

The Mehr news agency said that, due to unpaid bills, Iran stopped deliveries to Greek refiners Hellenic Petroleum and Motor Oil. Greece has long been the European Union country relying the most on Iranian oil--sometimes for as much as a third of its supplies.

The Mehr agency said Tehran may also cut shipments to Anglo-Dutch giant Shell because it has not paid for consignments equivalent to 8 million barrels since the beginning of 2012.

It said Shell has already halved its Iran oil shipments to 100,000 barrels a day.

"If the situation continues, Iran could cut oil exports to Shell as it has to the Greek companies Hellenic Petroleum and Motor Oil after they failed to fulfill payment commitments," Mehr said.

Motor Oil didn't return a request for comment.

A spokesman for Hellenic Petroleum declined to directly comment on the Iranian report but said "we have always proved that we are in a position to supply our refineries."

An oil-industry source said Shell was already on the cusp of stopping Iran oil purchases.

Shell has given notice on its one remaining contract with Iran and has no plans for further purchases of crude oil or refined products from Iran before the oil embargo, the industry official said.

An EU oil ban on Iran--aimed at forcing the Islamic Republic to curb its nuclear program--is set to come fully into force on July 1.

But a raft of sanctions on Iranian banks and shipping companies is already jeopardizing oil deliveries as buyers are having difficulties making payments and finding tankers for the crude.

Last month, Iranian crude exports fell by 300,000 barrels a day to 1.9 million barrels a day, according to preliminary data from oil-shipping consultancy Petro-Logistics SA.