Iran has entered the fight to retake a major Iraqi oil refinery from Islamic State militants, contributing small numbers of troops – some operating artillery and other heavy weapons – in support of advancing Iraqi ground forces, US defence officials said.

The US and its allies, meanwhile, have staged 22 air strikes on Isis targets since Friday, including four near Ramadi, the city taken by the militants this week, the US military said on Saturday. Coalition forces also attacked five Isis sites in Syria between Friday and Saturday.

Two US officials said Iranian forces had taken a significant offensive role in the Beiji operation in recent days, in conjunction with Iraqi Shia militia. The officials were not authorised to discuss the matter publicly and spoke on Friday on condition of anonymity.

One official said Iranians were operating artillery, 122mm rocket systems and surveillance and reconnaissance drones to help the Iraqi counteroffensive.

The Iranian role was not mentioned in a new US military statement asserting that Iraqi security forces, with US help, had managed to establish a land route into the Beiji refinery compound. The statement on Friday by the US military headquarters in Kuwait said Iraqis had begun reinforcing and resupplying forces isolated inside the refinery compound.

Iran’s role in Iraq is a major complicating factor for the Obama administration as it searches for the most effective approach to countering Isis. US officials have said they do not oppose contributions from Iran-supported Iraqi Shia militias as long as they operate under the command and control of the Iraqi government.

Friday’s US military statement quoted Brigadier General Thomas Weidley as saying that over the past three days Iraqi security forces and federal police have made “steady, measured progress” in regaining some areas leading to the Beiji refinery compound, in the face of suicide vehicle-borne bombs and rocket attacks. Weidley, chief of staff of the US-led military headquarters in Kuwait, recently described the oil refinery as a “key infrastructure and critical crossroads”.

The US statement said Iraqis, enabled by the US and its coalition partners, have “successfully cleared and established a ground route” into the refinery to resupply Iraqi troops. It listed US and coalition contributions as including air strikes, reconnaissance and the use of “advise and assist elements”.

Asked about the newly emerging role of Iranian forces in Beiji, the US command in Kuwait declined to comment directly, citing “operational security reasons”. It added that all forces involved in Beiji are “aligned with the government of Iraq” and under the control of Iraqi security forces.

Friday and Saturday’s strikes near Ramadi hit tactical units, armoured vehicles and a fighting position in militant-controlled territory. Ramadi fell to Isis on Sunday in a serious setback for Iraqi forces that also cast doubt on the US strategy of using mainly air strikes against the militants.

The other US-led attacks in Iraq were near the cities of al-Asad, Bayji, Fallujah, Haditha, Kirkuk, Makhmur, Mosul, Sinjar and Tal Afar. Isis tactical units, vehicles, fighting positions, heavy machine guns and buildings were hit.

In Syria, air strikes near al-Hasakah, Dayr Az Zawr, Kobani and Tadmur destroyed fighting positions, a tank and six anti-aircraft artillery systems, the joint task force said.

Separately, the Pentagon said on Friday that the cost of US military operations in Iraq and Syria since air strikes began in August was $2.44bn as of 7 May.

As well as the Beiji refinery, Isis fighters control the nearby town of Beiji, on the main route from Baghdad to Mosul, along the Tigris river.

The militants’ move on Beiji largely coincided with a successful offensive in Ramadi, the capital of Anbar province, last week. Iraqi forces withdrew from Ramadi on Sunday, leaving behind large numbers of US-supplied vehicles, including several tanks. The US said on Friday that its air strikes in Ramadi overnight hit an Isis fighting unit, destroying five armoured vehicles, two tanks and other military vehicles, as well as nine abandoned tanks and other armored vehicles.

Together, the Ramadi and Beiji losses have fuelled criticism of the Obama administration’s Iraq strategy and prompted the White House to authorise an acceleration of US weapons transfers to Baghdad, including expedited shipments of 2,000 shoulder-fired missiles for use against armoured suicide vehicles.

Iran had contributed advisers, training and arms to Iraqi Shia militias in an attempt to retake the city of Tikrit in March, but that effort stalled. In April, after the US joined the effort with air strikes, Iraqi security forces and allied Shia militias succeeded in regaining control of the city.

Tony Cordesman, a Middle East expert at the Center for Strategic and International Studies, said that while some in Tehran see the advantages of a Shia-led Iraqi government that deals equitably with the Sunni and Kurdish populations in order to achieve national unity, Iranian hardliners do not.

“At best, they are still pursuing a policy of competing with the United States for military influence over the Iraqi military and police, Shia militias, and even influence over Iraq’s Kurds,” Cordesman wrote in an analysis published Thursday. “At worst – and ‘at worst’ now seems more likely than ‘at best’ – Iran’s leaders are seeking an Iraq where Iran has dominant influence” after the Isis threat has been overcome.