"A number of contracts with Iraq have entered into force and are being fulfilled," the Interfax news agency quoted a source in Russia's defense export establishment as saying.
Deliveries of Mi-35 helicopter gunships and Su-25 fighters that provide close air support for ground troops have begun, added the source.
Iraq also has contracts for Mi-28 attack helicopters and mobile Pantsir-S1 surface-to-air and anti-aircraft artillery systems.
Russia's ambassador to Baghdad Ilya Mogunov had previously said he believed up to 10 Sukhoi fighter jets would be delivered by the end of the summer.
Russia and Iraq in 2012 signed contracts worth $4.2 billion (3.1 billion euros) to supply 36 of the Mi-28 attack helicopters and 48 of the Pantsir units, according to Russian Technologies (RosTec) which controls their producers.
Later it signed contracts for six Mi-35 helicopters and Su-25 fighters.
Iraqi officials said Wednesday that Defense Minister Saadun al-Dulaimi had left for Moscow in a bid to step up military cooperation.
"Dulaimi will meet the Russian defense minister and other officials to urge them to provide Iraq with weapons, equipment and modern military aircraft," Staff Lieutenant General Mohammed al-Askari told AFP.
The Russian defense industry source told Interfax that given the increased tensions following the downing of a Malaysian passenger jet over a region in Ukraine controlled by pro-Russia rebels, Washington may pressure Baghdad to cancel its orders for Russian weaponry.
Despite the billions of dollars spent on training and equipment by the United States during its eight-year occupation, Iraq's million-strong army completely folded when insurgents attacked last month.
Within days, the ISIL militants conquered Iraq's second city of Mosul and large swathes of the north and west.
NJF/NJF