ABU DHABI/HAMBURG, June 19 (Reuters) - Iran exported a 35,000 tonne cargo of wheat to Oman last week, traders said on Monday.

Iran's President Hassan Rouhani had said in September that the country was aiming to start exporting wheat soon after a good 2016 crop.

However, traders did not expect significant volumes to flow from the country.

"For the time being only one cargo of milling wheat has been traded to Oman," a European trader said.

"But because Iranian wheat is not graded, and with the current low prices of wheat from other more attractive origins, it is very unlikely that Iran will be able to sell more significant volumes."

Iran has been a major wheat importer in recent years as the country aimed to guarantee local food supplies, although its needs have varied due to erratic domestic production.

But Iran's Agriculture Ministry said last year that 4.2 million tonnes of wheat had been bought from domestic farmers in state-sponsored purchases, a 20 percent increase from the same period in the previous year.

(Reporting by Maha El Dahan and Michael Hogan, editing by Louise Heavens) ((Maha.Dahan@thomsonreuters.com; + 9712 4082101; Reuters Messaging: maha.dahan.thomsonreuters.com@reuters.net))