Iraq has asked the US to stage air attacks on Sunni insurgents as the Islamist fighters edged closer to full control of Iraq's largest oil refinery and continued to hold out against troops trying to retake the city of Tal Afar.

As the war to redefine the region's borders entered a second week, Iraq's foreign minister, Hoshyar Zebari, appeared on al-Arabiya television to issue the urgent plea: "We request the United States to launch air strikes against militants."

Witnesses at the Baiji refinery – between the cities of Mosul and Tikrit, both seized by the insurgent group last week – said insurgents broke through the perimeter of the site early on Wednesday and were within sight of administration buildings.

Their advance comes despite fierce resistance from Iraqi troops stationed at the refinery. There were reports that foreign security contractors had been sent to Baiji to protect what is one of Iraq's most important strategic assets. Many plant workers have been evacuated to Baghdad.

Losing control of Baiji would be a critical blow to Iraqi forces still reeling from the capitulation of close to 50,000 troops last week, many of whom have since been replaced by militias raised from the country's majority Shia population.

In Washington, General Martin Dempsey, chairman of the joint chiefs of staff, confirmed the US had received the request for air strikes. "We have a request from the Iraqi government for air power," Dempsey, told a Wednesday morning Senate hearing.

Obama is said to still be weighing military options, and US officials for days have quietly signalled that a decision is not imminent. But it will be harder for Obama to rebuke a formal entreaty from a besieged US partner, albeit a frustrating one.

However, Dempsey also told senators that the fluid state of the Iraqi battlefield has left the US with incomplete intelligence – a factor that makes an air campaign more difficult. "It's not as easy as looking at an iPhone video of a convoy and then striking it," Dempsey said.

Reuters reported that US officials, speaking on condition of anonymity, said that Iraq's request had included a call for drone strikes and increased surveillance by US drones, which have been flying over Iraq for some time. The Pentagon has said it stepped up surveillance, intelligence and reconnaissance efforts, at Baghdad's request.

In an interview with the Guardian, the Iraqi ambassador to the US, Lukman Faily, said the situation was critical, and warned of further bloodshed if Isis was not repelled. "Wherever they have the possibility, they will cleanse minorities, ethnic cleansing," he said. "Look at Mosul. They went into prisons, they executed the Shiite prisoners. They went into Mosul and they executed the Sunni imams who were reluctant about handing over their mosques to them. So what does that tell you? It tells you that they cannot coexist with others."

In Iraq, the spectre of full-blown sectarian war hangs heavily over those trying to decide how to deal with the crisis, with nationalistic aims often subsumed by sect loyalties. Many Shia volunteers heading to battle zones including Tal Afar say they see the insurgents more as a threat to their sect than to Iraq itself.

"Who do you think is running the war," asked a senior Iraqi official on Tuesday. "Those three senior generals who ran away? Qassem Suleimani [a leading Iranian general] is in charge. And reporting directly to him are the militias, led by Asa'ib ahl al-Haq."

Residents of Tal Afar, a city north-west of Mosul with a large Shia population, said reinforcements, most of them Shia irregulars, had been flown in to try to regain control from Islamic State of Iraq in Syria (Isis) jihadists who took the city on Monday.

The family of one fighter said he and most of his colleagues had been flown by government helicopter from the Dora refinery in Baghdad, where they worked as a protection force, to Tal Afar, flying straight over the besieged Baiji refinery. Baiji mainly supplies fuel to northern Iraq.

"It is providing 30% of oil resources to the country," said Qahtan al-Anbaki, an oil consultant. Most of it goes to Mosul and the north. It won't affect Baghdad or the south so much. The north is already seriously affected. Oil is three times the price it was a week ago in Mosul."

The grave threat to Baiji underlines how difficult it will be for the government to retake large swaths of land in the north and centre that were seized last week. Even with vastly inferior numbers, Isis has since consolidated its control of the areas using masses of equipment looted from military bases abandoned by fleeing troops.

The group's sphere of influence crosses well into Syria, where it controls eastern oilfields, and it uses their revenues to fund the fast-growing insurgency.

Battle lines for the defence of Baghdad have been drawn 40 miles to the north of the capital, near the city of Baquba, which remained a scene of intense clashes on Wednesday as jihadists again tried to enter the city centre. Their efforts to seize Baquba's prison have so far been rebuffed, with irregular militias rushed from Baghdad proving pivotal in the fighting.

Thousands of Iranians have volunteered to defend Iraq's Shia shrines. Iran is 90% Shia, a group considered to be apostates by Isis and other Sunni extremists. Iran's president, Hassan Rouhani, said the defence of Shia sacred sites in Najaf, Karbala, Baghdad and Samara was vital to his regime.

The Hezbollah leader, Hassan Nasrallah, said that because of the significance of the Iraqi shrines, the Lebanese group was "willing to sacrifice five times as much as we sacrificed in Syria", where his members, along with Iran, have led the fightback against rebel groups who have tried for more than three years to oust Bashar al-Assad.

The Syrian war has greatly amplified the threat from Isis in Iraq. However, the plains of Baquba and Anbar province in the country's far west were the original breeding ground of the group, which first rose to prominence in 2004 during a Sunni insurgency against US forces.

The Iraqi leader, Nouri al-Maliki, who is trying to assemble a political coalition to win a third term as prime minister, tried to assure the country that the momentum of the battle was with him. While Baghdad feels more assured than it was last week, some of the city's Sunni neighbourhoods remain paralysed. And on the Shia side of the Tigris river, militias have primacy over interior ministry or military forces.

Maliki pledged that Tal Afar would be retaken by Thursday, and fighting late on Wednesday appeared to be tipping the battle in favour of Iraqi forces. However, a fear remains that nothing decisive can be achieved without international intervention.

"If we got US drones to hit Baiji, and jets to bomb Isis elsewhere, we could slow them down," said a senior Iraqi MP. "Without them we can do nothing. Without them we can't win."