Fallon made the comments ahead of a meeting of ministers in Stuttgart on Wednesday, where he will discuss a further "package" of troops with his US counterpart Ash Carter. The troops are rumored to include engineers and advisers.
The news comes after a US Navy SEAL - a member of the force equivalent to the UK's Special Boat Service - was killed by enemy fire in Kurdish territory.
Fallon said Islamic State (IS, formerly ISIS/ISIL) is on the run, with Iraqi forces "retaking territory, hitting its finances and striking its leadership."
"Now is the time to build on recent success and we are looking hard at what more we can offer as Iraqi combat operations intensify," he said.
Comment: So if Iraq is successfully "retaking territory" from Daesh, why do they need US and British troops on the ground? Might it be to keep an eye on Iraq to thwart it from getting closer to Iran or Russia?















Comment: Further reading: Leaked documents reveal TTIP could tear asunder Europe's long-held environmental and consumer protections