ERBIL, Iraq (CBS News/CBSDC/AP) — The Sunni militant group in Iraq is a force roughly 3,000 strong and includes some Americans, a senior intelligence official told CBS News on Tuesday.

The majority of fighters in the group, the Islamic State of Iraq and Syria, are of Iraqi and Syrian origin.

In all, up to 10,000 are fighting with the group, 3,000 in Iraq and another 7,000 in Syria, the intelligence official said. Between 3,000 and 5,000 are foreigners, though how many of those are in Iraq is difficult to assess.

The fighters view Syria and Iraq as one battlefield and have been able to move swiftly inside Iraq with the help of local Sunnis, ties the intelligence official described as more of a “relationship of convenience” than a formal alliance.

The official said the group, also known as the Islamic State of Iraq and the Levant, was well-positioned to keep the territory that it has captured but would be stretched thin if it tried to push south into Baghdad. It has intentions to target U.S. interests, the official said.

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Its leader, Abu Bakr al-Baghdadi, rose through the ranks of the organization before becoming emir some time in 2010-2011. The group relies on a handful of senior decision makers, but al-Baghdadi has the final word, according to the intelligence official. Most of its funding comes via robbery, extortion and smuggling, with a small percentage coming from donations.

Meanwhile, Iraq’s top Kurdish leader warned visiting Secretary of State John Kerry on Tuesday that a rapid Sunni insurgent advance has already created “a new reality and a new Iraq,” signaling that the U.S. faces major difficulties in its efforts to promote unity among the country’s divided factions.

The U.N., meanwhile, said more than 1,000 people, most civilians, have been killed in Iraq so far this month, the highest death toll since the U.S. military withdrew from the country in December 2011.

Massoud Barzani, whose powerful minority bloc has long functioned as kingmaker in Iraqi politics, did not directly mention Prime Minister Nouri al-Maliki, who is facing the strongest challenge to his rule since he assumed power in 2006. But al-Maliki has made little effort beyond rhetoric to win the trust of his critics, who are led by disaffected Sunnis, Kurds and even several former Shiite allies.

Instead the Kurds have deployed their own well-trained security forces known as peshmerga and seized long-coveted ground of their own in the name of defending it from the al Qaeda breakaway group and other Sunni insurgents who have swept through the north. The Kurds are unlikely to give up that territory, including the disputed oil-rich city of Kirkuk, regardless of the status of the fighting.

Al-Maliki has been entirely focused on the security situation, spending hours each day in the main military command center, rather than politics, officials close to his inner circle say, speaking on condition of anonymity because they weren’t authorized to release such details. Despite the attention, Iraq’s mainly Shiite security forces have failed to wage any successful counteroffensives against the insurgents.

A weeklong fight for control of Iraq’s largest oil refinery continued Tuesday with helicopter gunships attacking what appeared to be formations of Sunni militants preparing for another assault on the facility in Beiji, a top military official said.

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Chief military spokesman Lt. Gen. Qassim al-Moussawi has denied reports that the facility has fallen to the rebels.

Government air forces also reportedly bombed the town of Qaim near the Syrian border on Tuesday, days after it was seized by Islamic extremists in Anbar province, west of Baghdad. Provincial government spokesman Dhari al-Rishawi said 17 civilians were killed.

Kerry traveled to Erbil, the capital of the self-rule Kurdish region on Tuesday, a day after meeting with al-Maliki and other Iraqi officials in Baghdad, where he pushed for them to adopt new policies that would give more authority to Iraq’s minority Sunnis and Kurds.

Kerry said after the Baghdad meetings that all the leaders agreed to start the process of seating a new parliament by July 1, which will advance a constitutionally required timetable for naming a president, prime minister and a new cabinet. Al-Maliki’s political bloc won the most seats in parliamentary elections in April but must assemble a majority coalition in the legislature in order to secure a third term for the Shiite leader.

Kerry has repeatedly said that it’s up to Iraqis – not the U.S. or other nations – to select their leaders. But he also has noted bitterness and growing impatience among all of Iraq’s major sects and ethnic groups with al-Maliki’s government.

Barzani’s support will be crucial for resolving the political impasse because Kurds represent about 20 percent of Iraq’s population and usually vote as a unified bloc.

He told Kerry that Kurds are seeking “a solution for the crisis that we have witnessed.” But, he said, “we are facing a new reality and a new Iraq.”

Barzani did not elaborate, but he was apparently referring to the Kurds now controlling Kirkuk and other areas in northern Iraq that they have long sought to incorporate into their region.

Kerry said at the start of an hour-long meeting that the Kurdish security forces have been “really critical” in helping restrain the insurgents.

“This is a very critical time for Iraq, and the government formation challenge is the central challenge that we face,” Kerry said. He said Iraqi leaders must “produce the broad-based, inclusive government that all the Iraqis I have talked to are demanding.”

The U.S. believes a new power-sharing agreement in Baghdad would soothe anger directed at the majority Shiite government, a rage that is thought to have fueled the ongoing insurgency. Iraq’s population is about 60 percent Shiite Muslim, whose leaders rose to power with U.S. help after the 2003 fall of former President Saddam Hussein and his Sunni-dominated regime.

Two senior State Department officials who attended the meeting said Kerry pre-emptively brought up the issue of the Kurdish region’s “self-determination” – its years-long desire to create an independent state – and told Barzani that Iraq will remain stronger if it is united. They spoke on condition of anonymity in exchange for releasing the details of the private meeting.

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Iraqi Kurds had no love for Saddam, and were allowed to carve out a semi-autonomous region in Iraq’s north to protect themselves from his policies. But Barzani for years has feuded with al-Maliki, most recently over the Kurdish regional government’s decision to export oil through Turkey without giving Baghdad its required share of the revenues.

The Kurdish region is home to several vast oil fields and has enjoyed security and economic stability unmatched across the rest of the Iraq.

Control of Kirkuk and Kurdish pockets elsewhere in northern Iraq has been at the heart of tension between the Kurdish region and the Baghdad government. Al-Maliki’s supporters frequently suggest that the Kurds did nothing as the Sunni militants swept through most areas in the north because they stood to gain from chaos in the region. The Kurds have insisted they moved to Kirkuk and other areas to fill a security vacuum.

Al-Maliki has for months requested U.S. military help to quell the insurgency, and the Obama administration has said it must respond to the insurgent threat before it puts the West at risk of attack.

Obama is reluctant to send American military might back to the war zone, although U.S. special forces have been ordered to Baghdad to train and advise Iraqi counter-terror soldiers.

The U.N. findings were the first concrete sign of the toll the chaos is taking on civilians and Iraqi security forces.

Its team reported at least 1,075 people killed, including 757 civilians in the Ninevah, Diyala and Salahuddin provinces in northern and central Iraq, from June 5 through Sunday.

U.N. human rights office spokesman Rupert Colville cautioned however that the figure “should be viewed very much as a minimum,” and said it included “summary executions” and extra-judicial killings of civilians, police and soldiers who had signaled that they were no longer combatants.

In violence Tuesday, assailants killed Munir al-Qafili, the head of the Kirkuk city council and a politically active member of the Turkmen minority group, police chief Torhan Abdul-Rahim said. It was the first such attack since Kurdish forces seized control of the city.

West of Baghdad, authorities found the bodies of 12 policemen killed as militants seized the Anbar town of Rutba this weekend. Militants also stole at least 6 billion Iraqi dinars, about $5 million, from the town’s state-run bank, the authorities said, declining to be identified because they were afraid of retaliation by the militants.

The bodies of three men who were shot in the head and chest and had their hands and legs bound also were found on the streets of three Shiite neighborhoods in and around Baghdad, according to police and hospital officials.

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