The United States says Iranian F-4 Phantoms have carried out bombing raids against Isis north-east of Baghdad, a claim that appears to be confirmed by film of the aircraft taken from the ground.

Iran, however, denies that any of its planes are carrying out combat missions in Iraq. The raids are said to have taken place in Diyala province on the border with Iran, where there has been heavy fighting for months between Isis fighters, Shia militias and Kurdish Peshmerga. Isis has recently been driven out of the towns of Jalawla and Saadiyah.

An Iraqi security expert, Hisham al-Hashimi, told a news agency that 10 days ago: “Iranian planes hit some targets in Diyala. Of course, the government denies it because they have no radars.” Film appears to show an F-4 in action, a type of aircraft only used by Iran and Turkey.

It is not clear why Iran should have used its air force for the first time in Iraq, though it has been giving heavy publicity to the role of Qasem Soleimani, the head of the Quds Force of the Islamic Revolutionary Guards, in inspiring and organising Shia militias.

Having long remained in the shadows, Mr Soleimani began to allow himself to be photographed and filmed in company with militia commanders. The militias are the main fighting force of the Baghdad government whose 350,000-strong army disintegrated when attacked by Isis in northern and western Iraq over the last six months.

The US and Iran were quick to deny that they are co-ordinating military action against Isis, though they are pursuing parallel policies in seeking to defend the governments in Baghdad and Irbil. The Pentagon spokesman Rear Admiral John Kirby told a news briefing on Tuesday that the United States was not co-ordinating its military activities with Iran, and added that it was up to the Iraqis to manage Iraqi air space.

“It’s the Iraqi air space and [Iraq’s] to deconflict. We are not co-ordinating with nor are we deconflicting with Iranian military,” Admiral Kirby said. However, it is likely that, if Iranian aircraft were in action, Iran would have told Baghdad what they were doing and the Iraqi military would have passed this on to the Americans.

John Kerry would not confirm that Iran had launched the strikes, saying it was “up to them or up to the Iraqis to do that, if indeed it took place”. He said that if Iran did decide to launch strikes against Isis then the “net effect is positive”.

US-Iranian policy in Iraq has been a mixture of open confrontation and covert co-operation since the overthrow of Saddam Hussein, whom both governments opposed in 2003. Today, they both want to stop and, if possible, eliminate Isis and at the same time expand their own influence.

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The recently displaced Prime Minister Nouri al-Maliki remained in power for eight years because he was able to win the support of Washington and Tehran despite the extreme incompetence and corruption of his government. The US and Iran both eased the process of forcing him to leave office though he remains a force. He recently made a trip to Iran, where was received at the highest level.

The Iranian denial that its planes had conducted air raids was categorical as it was its rebuttal of any suggestion that it is co-operating with the US in Iraq. “Iran has never been involved in any air strikes against Daesh [Isis] targets in Iraq. Any co-operation in such strikes with America is also out of the question for Iran,” a senior official said.

The Iraqi Prime Minister, Haider al-Abadi, in Brussels for a meeting of the US-led coalition against Isis, said he was not aware of any Iranian air strikes. The US Secretary of State, John Kerry, said the US-led coalition had inflicted serious damage on Isis, carrying out around 1,000 air strikes so far in Iraq and Syria, but the fight against the militants could last years.

Both Washington and Tehran were horrified when the Iraqi government suffered a complete defeat at Mosul on 10 June when attacked by much smaller Isis forces.

The US had spent years training the Iraqi army only to see it dissolve without fighting. Mr Maliki was increasingly seen as being under Iran’s influence, but it was a severe blow to Iran to watch the Shia-dominated government in Iraq collapse as the Sunni Arabs revolted. This brought America back as an important player in Iraq whose aid was once more badly needed by Baghdad and Irbil.

The Baghdad government now rules a Shia rump state that does little without conferring with Iran. When Isis attacked the Iraqi Kurds on 1 August and defeated the Peshmerga, so threatening Irbil, the US stepped in with air strikes and Iran sent advisers and artillery, say Kurdish sources.

The knowledge that at the end of the day the US and Iran will step in to prevent an Isis victory has done much to restore Iraqi army and Kurdish morale that had been undermined by Isis’s terror tactics and surprise assaults.