According to Fallon, more than 30 extra troops have been authorised for deployment to training locations at Besmayah and Taji, two of the five coalition-led building partner capacity (BPC) sites in Iraq.
The troops are expected to provide training in areas such as logistics and bridge-building, as well as specialist medical staff.
Fallon said: "We’ve seen solid progress against Daesh in Iraq in recent months. Now is the time to step up our training of Iraqi Forces, as they prepare for operations in key cities such as Fallujah and Mosul.
"Along with the trebling of UK air strikes, this underlines the crucial role our armed forces are playing in the fight against Daesh."
The deployment will bring the total number of UK training personnel in Iraq to more than 300, and the number of soldiers engaged in the theatre to more than 1,000.
The UK has already been training the Iraqi forces in areas including infantry skills, counter-improvised explosives and weapons maintenance.
The defence secretary said that such training programmes ‘have saved lives and supported recent successful operations on the ground, such as the retaking of Ramadi’.
So far, the British army has helped train more than 6,500 personnel in Iraq.
Image: A Kurdistan troop takes part in training delivered by British soldiers in Erbil, Iraq. Photo: courtesy of UK Government.