The crisis in Iraq escalated rapidly on Thursday as Iraqi Kurdish forces took control of key military installations in the major oil city of Kirkuk and the Sunni jihadi group Isis revealed its intention to move on Baghdad and cities in the southern Shia heartland.

Kurdish peshmerga fighters entered Kirkuk after the central government's army abandoned its posts in a rapid collapse during which it lost control of much of the country's north.

Iraq has been fragile since the 2003 US-led invasion and the latest developments have raised fears that it is in danger of splintering along ethnic and sectarian lines.

Iraq has a Shia majority, with a substantial Sunni minority concentrated in Baghdad and the provinces north and west, who have long complained of being disenfranchised. Iraqi Kurds enjoy a large degree of autonomy and self-government in the north-east but have long coveted Kirkuk, a city with huge oil reserves which they regard as their historical capital.

In Kirkuk, truckloads of peshmerga fighters patrolled the streets, but sporadic clashes continued between Kurdish forces and Isis gunmen on the outskirts of the city. A Kurdish minister responsible for regional security forces survived a bomb blast as he drove to the city after visiting peshmerga units in the surrounding region, AFP reported. Since Tuesday, black-clad Isis fighters have seized Iraq's second biggest city, Mosul, and Tikrit, hometown of the former dictator Saddam Hussein, as well as other towns and cities north of Baghdad. They continued their lightning advance on Thursday, moving into towns just an hour's drive from the capital.

About 500,000 people have fled Mosul, home to 2 million, and the surrounding province, many seeking safety in autonomous Kurdistan.

Isis's spokesman, Abu Mohammed al-Adnani, said on Thursday that the group's fighters intended to take the southern cities of Kerbala and Najaf, which hold two of the holiest shrines for Shia Muslims.

US officials have said they are considering ways to help the Iraqi government even as it emerged that the Obama administration had rebuffed a secret request from the Iraqi prime minister, Nouri al-Maliki, to bomb Isis positions.

Reports from Iraq have painted a confused picture of a rapidly developing situation with fighting reported in a number of key locations on Wednesday night and on Thursday, including on the outskirts of the city of Samarra, where government officials said Isis fighters had been driven back.

According to Army Staff Lieutenant General Sabah al-Fatlawi, quoted by Agence France-Presse, "elite forces" backed by air strikes pushed back a "fierce attack by Isis fighters who then bypassed the city heading towards Baghdad".

Complicating the picture of the past few days were emerging suggestions that other Sunni insurgent groups, including Ba'ath nationalists, supporters of the executed Saddam, had played a role in the series of stunning setbacks for the Iraqi military.

The sudden collapse of the Iraqi army has raised international concerns about a rapidly widening regional crisis that has implications for Iraq's powerful neighbours, Iran and Turkey.

Iran's president, Hassan Rouhani, warned in a televised address on Thursday that Iran would combat the "violence and terrorism" of Sunni extremists in Iraq. The foreign minister, Mohammad Javad Zarif, offered Iran's support for Iraq's "fight against terrorism" during a phone call with his Iraqi counterpart, Iranian state TV reported.

In Baghdad residents described panic buying and rising fear.

A meeting of MPs called by Maliki to vote on introducing an emergency law was cancelled after insufficient MPs attended.

The Iraqi leader – a Shia whose authoritarian and sectarian policies have been blamed by many as the root cause of the country's crisis – is trying to hold on to power after indecisive elections in April. The mounting sense of anxiety in the capital followed a statement by a spokesman for Isis who said the group had scores to settle with Maliki's government.

Hundreds of young men crowded in front of the main army recruiting centre in Baghdad on Thursday after authorities urged Iraqis to help battle the insurgents.

The army of the Shia-led government in Baghdad has essentially fled in the face of the onslaught, abandoning buildings and weapons to the fighters who aim to create a strict Sunni caliphate on both sides of the Iraq-Syria border.

In Tikrit, militants have set up military councils to run the towns they captured, residents said. "They came in hundreds to my town and said they are not here for blood or revenge but they seek reforms and to impose justice," said a tribal figure from the town of Alam, north of Tikrit. "They picked a retired general to run the town. 'Our final destination will be Baghdad, the decisive battle will be there,' that's what their leader of the militants group kept repeating."