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But there was scepticism about the ability of Zernomir to deliver on the deal from the start.
"The deal was cancelled due to difficulties in banking operations and execution," the government source said.
A Russian agriculture ministry official had told Reuters the main problem was that the supplier lacked experience and had set the price too low.
State grain buyer the General Authority for Cereal Processing and Trade (Hoboob) instead signed contracts in February with local traders for around 1.2 million tonnes of Russian wheat.
"We now have within our hands a lot of the quantities from those contracts and we will also evaluate the situation and see whether we need to go back to the market through tenders," the source said.
Flat bread is a subsidised staple in Syria, where war is estimated to have killed several hundred thousand people and forced millions to flee their homes.
Hoboob has not named the Syrian firms that are helping it buy Russian wheat.
Syria's strategic wheat reserves stand at six months' worth versus just 17 days of reserves last year, Internal Trade and Consumer Protection Minister Abdullah al-Gharb said last month.
(Reporting by Maha El Dahan; additional reporting by Polina Devitt in Moscow; editing by Christian Schmollinger and Jason Neely)