US secretary of state John Kerry has urged Kurdish leaders to stand with Baghdad and insisted that the imminent deployment of American military forces is "not intervention" in Iraq's affairs.

As fighting continued for control of Iraq's largest oil refinery at Baiji, Kerry flew to the Kurdish region on an emergency trip through the Middle East amid fears that Iraq faces disintegration under the onslaught by Islamist militants – the Islamic State in Iraq and the Levant (Isis) – backed by disgruntled Sunni tribes.

In an interview with American journalist Andrea Mitchell, Kerry diminished the deployment of up to 300 irregular forces, expected to come largely from US army special forces.

"Well, that's not intervention," Kerry said.

Kerry characterized the so-called "advisory" mission – "planning, advising, some training and assisting" – as something short of intervention, since "we are not here in a combat role. We are not here to fight. And the president has no intention – none whatsoever – of returning American combat troops in Iraq to go back to where we were."

Ninety of those troops, organized into four teams, arrived in Baghdad on Tuesday to begin establishing a "joint operations center" with the Iraqi military, Pentagon press secretary Rear Adm. John Kirby said. They join 30 "advisers" already there on secondment from the US embassy.

Kerry's visit came as the UN said at least 1,075 people, mostly civilians, have been killed since the insurrection began 17 days ago. The spike in violence is sure to make June the deadliest month in Iraq since early 2008.

Monthly violence had been increasing in Iraq since the start of the year and rapidly deteriorating security in the west, centre and north of the country means the trend is likely to continue.

US officials believe that persuading the Kurds to stick with the government in Baghdad will help keep Iraq together. "If they decide to withdraw from the Baghdad political process, it will accelerate a lot of the negative trends," said a senior state department official.

But Massoud Barzani, the Kurdish president, hardly provided a ringing endorsement for the Iraqi government.

"We are facing a new reality and a new Iraq," said Barzani at the start of his meeting with Kerry. Earlier, he blamed prime minister Nouri al-Maliki's "wrong policies" for the violence and called for him to quit, saying it was "very difficult" to imagine Iraq staying together.

Kurdish troops have taken control of Kirkuk, which was abandoned by the Iraqi army after Isis forces seized Mosul at the beginning of a lightning campaign. The Kurds consider Kirkuk – just outside their autonomous zone – their historic capital; its capture makes it more tempting for the Kurds to go it alone rather than sticking with an unpopular and tottering regime.

The Kurdish region is home to several vast oilfields and has maintained stability, in stark contrast to the rest of Iraq. Senior Kurdish officials have said privately that they are no longer committed to Iraq and are biding their time for an opportunity to seek independence.

In an interview with CNN, Barzani repeated a threat to hold a referendum on independence, saying it was time for Kurds to decide their own fate. Tuesday's meeting in Irbil, the Kurdish capital, came a day after Kerry travelled to Baghdad to discuss options with Sunni and Shia leaders, including Maliki.

Kerry said after the Baghdad meetings that all the leaders agreed to start the process of forming a new government by 1 July, which will advance a constitutionally required timetable for distributing power among Iraq's political blocs, divided by sect and ethnicity. Barzani's support is key to solving the crisis. Kurds represent about 20% of Iraq's population and usually vote as a unified bloc.

Kerry, in a series of Tuesday interviews, did not indicate any imminent airstrikes. His primary focus is to urge Iraqi leaders to form a government with sufficient Sunni support that can capitalize on any military setbacks dealt to Isis, something Kerry said was "happening very rapidly right now."

While the initial wave of 130 advisers out of up to 300 expected may not engage in direct combat, their impending arrival in Iraq kicks off a deeper US involvement in Iraq's crisis. They are a vanguard, involved not only in designing and aiding a defense of Baghdad against Isis currently led by Iran, but gathering situational intelligence to supplement the aerial surveillance of Sunni Iraqi territory seized by the jihadist army, and potentially spotting for US air strikes.

The Pentagon has been tight-lipped about what equipment the "advisory" teams will bring, but Kirby has said they will be armed and possess the right to defend themselves. Iraq has granted them diplomatic assurances about their legal protections from local courts, Kirby said, clearing their entry into Baghdad. A lack of such assurances prompted the 2011 US troop withdrawal.

Kirby described the special operators' mission as "limited" and "short-term," obviating the need for a formal legal arrangement. "It's not meant to be a long-term permanent mission," he said.

While consistently declaring that the US will neither choose a new Iraqi leader nor oust Prime Minister Nouri al-Maliki, whom US officials consider a failure despite the US helping install him in 2006, Kerry suggested that the air strikes Iraq desires will not occur before a new government takes power.

"If the President were to just make some decision to strike here or there, there's no backup, there's no 'there' there in the Iraqi government, it could be completely wasted. It's not a pathway to victory. So what you need to do first is get the government formation done here in Iraq," he told CBS' Margaret Brennan.

Although Kerry said that the advance of Isis across Iraq did not grant the jihadist organization "a safe haven at this point in time," the chief US diplomat suggested that a forthcoming and concerted regional response would aim to confront Isis. Over the past two weeks, Isis has seized major cities and towns across Sunni Iraq and effectively erased borders with Syria and Jordan.

The Baiji refinery, a strategic industrial complex in northern Iraq, remained a frontline early on Tuesday. Militants said late on Monday they had seized it, but two government officials said troop reinforcements had been flown inside the compound and fended off the assault.

Local tribal leaders said they were negotiating with both the government and Sunni fighters to allow the tribes to run the plant if Iraqi forces withdraw. One of the government officials said Baghdad wanted the tribes to break with Isis and other Sunni armed factions, and help defend the compound. The plant has been fought over since last Wednesday, with sudden reversals for both sides and so far no clear victor.