On one side were Kurdish fighters, dug in behind a series of ramparts and trenches reminiscent of the first world war. Five hundred metres away, over a muddy canal and past a farm, were the jihadist fighters of Isis (Islamic State).

Offering a pair of binoculars, first lieutenant Noman Osman, a Kurdish soldier, pointed to the Isis checkpoint. It was a canopied shed. Nearby, on a deserted road, was a burnt-out lorry. There was also an American Humvee, looted from Iraqi forces by the Islamist fighters. Beyond that, a ridge of feathery trees from where Isis snipers had been taking potshots at Kurdish positions.

"Our mission is defensive. We are defending our land from terrorists," Osman explained. "We don't venture beyond the canal." What did he think of his opponents, who now control much of Sunni Iraq? "Isis are traitors," he declared. "No cars cross here. But two days ago a Sunni sheikh came to visit. He says he wants to fight Isis, that locals are fed up with them."

From a Kurdish watchtower – reached via a metal ladder – a few civilian vehicles were visible in the far distance. The agricultural landscape revealed sunflower fields, irrigation ditches, and a line of pylons. The stillness was deceptive. Removing his hat, Osman showed off a bullet wound. A jihadist militant shot him last month, he said. "After two weeks in hospital, I went back to the front," he added.

This frontline at Mariam Bek marks the new 1,000km faultline along which Iraq is fracturing. On one side is the Islamic State, the new caliphate proclaimed by Isis, across Syria and Iraq. On the other, a possible future state of KurdistanIsis and the Kurds now confront each other across a swathe of territory from Sinjar region in the northwest, next to Syria, through to Khanaqin, close to the border with Iran. Most of the villages here are Kurdish. But they are also home to Yazidis, Christians, Turkmens and Arabs.

"When the British set up this country in the 1920s they didn't do a good job," said Colonel Ghaleb Taha Ismail, the chief of police in Kirkuk's Kurdish Rahim Awa neighbourhood. "Before they were three provinces – Baghdad, Mosul and Basra. I think it will be three provinces again. History will go back to its original format."

Why? "Iraq has been a country for 90 years. Throughout this period, these three provinces haven't been able to live together."

Ismail, a Kurd, who took over as police chief in January, said he presided over a multi-ethnic force. It included Kurds and other groups. "The people of Kirkuk should vote to decide their future. I believe in democracy," he said. Meanwhile, his uniform still bore the insignia of Iraq's interior ministry. Hanging in the entrance lobby were framed portraits of officers murdered in the line of duty. They had been killed in the on-off insurgency waged by Sunni militants, since the US-led invasion of Iraq in 2003, he said.

Kurdish moves to peel away from Baghdad's rule are multiplying. They have announced a referendum, and on Friday said they were pulling out of Iraq's national government, no longer sitting in the cabinet or ministries.

Central to this new reality is Kirkuk, an oil-rich, mainly Kurdish city of around a million people, which lies outside the Kurdish autonomous region. But the Kurds have largely controlled it since 2003.

On Friday peshmerga (Kurdish fighters) seized two nearby oilfields, Kirkuk and Bai Hassan, turfing out Arab workers and replacing them with their own staff. Baghdad's oil ministry was furious.

The move consolidates the Kurds' hold on Kirkuk and its huge oil reserves. It suggests that the Kurdish fighters who entered the city a month ago are not planning to leave.

They moved in after the Iraqi troops tasked with guarding it ran away. The alternative, the Kurds say, was an Isis takeover, followed by a bloodbath. Elsewhere, the peshmerga advanced somewhere between 20km and 40km beyond existing Kurdistan and deep into federal Iraqi territory. Kurdistan got bigger; so did its security headache.

Despite heavy security around the city, a suicide car bomb blew up outside a police station in the Huzairan district on Friday, killing at least nine and injuring 21. Last month an Isis suicide bomber killed six.

The Kurdish security agency Asayish says the situation inside Kirkuk is now "relatively calm". But it admits that Isis remains a potent threat.

Spokesman Captain Farhad Hama Ali said fighting was going on in two areas immediately south of the city: the subdistrict of Mala Abdulla, which has a mixed population of Arabs and Turkmen, and the contested village of Besir. "Isis still wants to take Kirkuk. It wants to turn it into another Ramadi," he warned.

According to Ali, politicians in Baghdad were to blame for the extraordinary rise of Isis. Ali said the Kurds had warned Baghdad five days before the fall of Mosul that Isis was on the march. The federal government ignored the tip and told the Kurds to stay out of the city, Iraq's second biggest. When Isis did surge in, Baghdad called and desperately asked for assistance. "By this point it was too late," Ali said.

In theory, Kirkuk is still under central control. The Iraqi flag flies above the governor's heavily defended mansion together with the flag of Kurdistan. Photos in the lobby show Kirkuk's development over the past century: a brief period of British occupation in 1918; the discovery of oil in the 1920s; modernisation of what was once ancient Sumeria and Assyria. The ethnic balance continues to change. In the 1980s many Kurds fled Saddam's murderous Anfal campaign. Arab settlers arrived. Over the past decade, Kurds have come back.

Many feel the moment of Kurdish destiny has arrived. Last week the president of Iraqi Kurdistan, Massoud Barzani, called on the Kurdish parliament to hold a rapid referendum. It is likely to take place in two stages. The first will be a vote on whether Kirkuk and other disputed territories should join the autonomous Kurdish region. The second – to be held later this year, or possibly early next – will decide whether Kurdistan should break away from Baghdad.

Iraq's disintegration has affected the city in multifarious ways. It has, for example, touched on the fortunes of Kirkuk's football club. Nowzad Qader, the head of Kirkuk's FA, said Iraq wasn't able to complete its league this year, with players unable to travel to Baghdad. It was too dangerous, he said, since Isis controlled the road. "Isis doesn't like humanity much, let alone football," he observed. "If Iraq still exists next season we'll resume."

Nearby, youths kicked a ball around in the early evening heat.

Qadar said the local FA reflected Kirkuk's tradition of coexistence, at odds with the sectarian mayhem in the rest of the country. He was a Kurd, his deputy a Turkman and the secretary an Arab. "It's like a microcosm of Iraq. We work together in brotherhood," he declared. Maureen Nikola, a volleyball coach, said girls who played on her team came from all of Kirkuk's ethnic groups. Some of her Christian players had emigrated with their families after 2003, she said. Nikola, a Christian herself, added: "If the peshmerga weren't here, we would have had to flee, like Mosul."

Back at the frontline, first lieutenant Osman said morale was high among his men, who were posted along sandbagged embrasures or who sheltered under tarpaulins from the afternoon sun. He declined to say how many of them had been killed. "My request to Britain is to help the Kurds to defeat terrorism," he said. "We have old weapons. We need new ones." Osman said hi-tech military equipment given by the US to the Iraqi army had fallen into the hands of Isis. "We told them [the Americans] this would happen and it did," he said.

Hadn't western military involvement in Iraq been a disaster, though? "We're not talking about Iraq. We are talking about Kurds," Osman said. "Kurds have always been friends of the UK. When the US and Britain came to Iraq, the Kurds welcomed them with flowers. The rest of Iraq welcomed them with IEDs."

Either way, the rise of Isis was now the west's problem, he suggested. "They are a threat to the UK and other countries. There are 500 Brits fighting with Da-ash [Isis] right now," he said.

On the Isis side of the canal, nothing moved. The Islamist fighters appeared to be having a break. On the peshmerga side, it was quiet too – other than a love song by the Kurdish-British singer Mazhar Khaleqi. "The Ba'athists want to set up their own region, their own fundamentalist state," Osman said. "We have our demands too: an independent country."

Additional reporting by Fazel Hawramy