Bashneft and Vietnam's PetroVietnam were part of a consortium led by UK's Premier to bid for Block 12 in Iraq's fourth energy bidding round in May.
The consortium rejected the government's proposed fee of $5 per barrel of oil equivalent as too low and sought $9.85 for each barrel.
The deputy director of the Oil Ministry's contracts department, Sabah al-Saidi, said that the ministry reached a separate agreement with Bashneft last week after it accepted the $5 fee.
The 8,000-square-kilometer (3,100-square-mile) block is in the southern provinces of Muthanna and Najaf.
The May auction was Iraq's fourth since 2009 and was meant to attract foreign investment in the country's crucial energy sector, particularly natural gas exploration.
It drew lukewarm response from foreign companies due to tough contract terms. Out of 12 exploration blocks were on offer only three were awarded.
Only areas with undetermined hydrocarbon resources were on offer, while previously the rights to known large and medium oil and gas fields were being auctioned off.
Iraq has offered only service contracts in which companies are paid a flat fee, rather than deals in which they receive a share of the hydrocarbons found.
The three successful bids were made by consortiums led by Kuwait Energy, Russia's Lukoil and Pakistan Petroleum.
Kuwait Energy with its partners, Turkey's TPAO and the UAE's Dragon Oil, will explore for oil in southern Basra province and will be paid $6.24 for each barrel of oil equivalent it finds.
Russia's Lukoil and Japan's Inpex Corp. will explore for oil in southern Iraq and will be paid $5.99 for each barrel of oil equivalent they find and Pakistan Petroleum will search for natural gas in the east of the country and is to receive $5.38 for each barrel of oil equivalent.
All three deals will be initially signed in mid-July and will be sent to the Cabinet for final approval, al-Saidi said. The fourth deal could be initially signed later this month, he added.
Iraq is trying to build up its energy sector, hit by years of neglect and violence, including the turmoil following the ouster of Saddam Hussein in 2003.
Iraq holds the world's fourth largest oil reserves of 143.1 billion barrels, and oil revenues cover nearly 95 percent of the country's local budget.
Since 2008, Iraq has awarded 15 oil and gas deals to international energy companies, the first major investments in the country's energy industry in more than three decades.
Daily oil production stands at about 3 million barrels. Iraq initially set a target of 12 million barrels a day by 2017, but it is now considering a downward revision to fewer than 10 million barrels, in part because of infrastructure bottlenecks.