The United Kingdom, which is supporting US-led air strikes aimed at driving IS jihadists out of significant parts of Iraq, is already training Kurdish forces in the country.

"We will be stepping up our training effort. We're talking to our coalition partners about how the... additional training is going to be provided, in training centres in and around Baghdad," Fallon told journalists in the Iraqi capital.

The training would be for battalions able to leave the front lines, he said, without specifying if it would involve Iraqi soldiers, police or both.

The exact number of trainers that would be sent had not yet been decided.

"One particular area of expertise we have is in counter-IED (improvised explosive devices). We've learnt from Afghanistan in dealing with roadside bombs and car bombs and we have some specialist knowledge to contribute," said Fallon.

Britain already has a "small number of people" in Baghdad, and "will be looking now to see how we can strengthen that, the liason work that we're doing in the ministries and the security agencies here," he said.

The Ministry of Defence said last month that a "small, specialist team" of soldiers was providing training to Kurdish forces in the country's autonomous north on the use of heavy machineguns.

And it said in a statement on Wednesday that Britain would be increasing the training on offer to the Kurds "to include infantry skills such as sharp-shooting and first aid, alongside the provision of further equipment".

Fallon met with Prime Minister Haidar al-Abadi, Kurdish regional president Massud Barzani and other senior Iraqi and Kurdish officials during the trip, on which he visited both Baghdad and the northern city of Arbil, the ministry said.

Prime Minister David Cameron has ruled out sending combat troops back into Iraq, wary of committing to a new conflict six months from a general election.

Britain was one of the main members of the US-led "coalition of the willing" that invaded Iraq in 2003 and overthrew dictator Saddam Hussein.

The last British forces withdrew from Iraq in 2011.

Britain has not participated in air strikes by the coalition against IS in Syria, where the jihadist group has also seized significant territory.