A spokesman for the Iraqi prime minister, Nouri al-Maliki, has said he will not stand down as a condition of US air strikes against Sunni militants who have made a lightning advance across the country.

Iraq's foreign minister, Hoshyar Zebari, on Wednesday made a public call on al-Arabiya television for the US to launch strikes, but Barack Obama has come under pressure from senior US politicians to persuade Maliki, a Shia Muslim who has pursued sectarian policies, to step down over what they see as failed leadership in the face of an insurgency.

Dianne Feinstein, the chair of the Senate intelligence committee, told a hearing on Wednesday that Maliki's government "has got to go if you want any reconciliation", and Republican John McCain called for the use of US air power but also urged Obama to "make very clear to Maliki that his time is up".

The White House has not called for Maliki to go but its spokesman Jay Carney said that whether Iraq was led by Maliki or a successor, "we will aggressively attempt to impress upon that leader the absolute necessity of rejecting sectarian governance". The US secretary of state, John Kerry, said Washington was focused on the Iraqi people, not Maliki.

Maliki's spokesman, Zuhair al-Nahar, said on Thursday that the west should immediately support the Iraqi government's military operation against Islamic State in Iraq and the Levant (Isis) rather than demand a change of government. He insisted that Maliki had "never used sectarian tactics".

"Our focus needs to be on urgent action – air support, logistic support, counter-intelligence support to defeat these terrorists who are posing a real danger to the stability of Iraq, to the whole region," he told the BBC Radio 4 Today programme.

Obama is said to be still weighing military options, and US officials for days have quietly signalled that a decision is not imminent.

General Martin Dempsey, chairman of the joint chiefs of staff, confirmed that the US had received the request for air strikes but said that the fluid state of the Iraqi battlefield had left the US with incomplete intelligence, a factor that made an air campaign more difficult. "It's not as easy as looking at an iPhone video of a convoy and then striking it," he told senators.

Fighting continued in Iraq on Thursday as Isis militants raised their black banners at Iraq's largest oil refinery. A witness told Reuters that militants were manning checkpoints around the Baiji facility and that a huge fire in one of its tankers was raging. A security official in Baghdad said government forces were still inside the complex.

Witnesses at the Baiji refinery – between the cities of Mosul and Tikrit, both seized by Isis last week – said insurgents had broken 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.

Maliki announced on Thursday that volunteers who fought in "hot areas" with the country's security forces would be given 750,000 Dinars ($644) a month. Non-fighting volunteers will be paid 500,000 Dinars ($450) and all volunteers will be given an extra 125,000 Dinar ($107) food allowance per month, a statement said.

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 Shia 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 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, Kerbala, Baghdad and Samarra 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.

Maliki, who is trying to assemble a political coalition to win a third term as prime minister, has tried to assure the country that the momentum of the battle is 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, the 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."