Members of the all-volunteer Iraq of Imam Hussein Regiment take up positions on a street corner as part of a basic-training course in the Iraqi holy city of Karbala. Shiite men have been ordered by Grand Ayatollah Ali Sistani, the country’s highest Shiite authority, to protect Shiite shrines and help counter the recent gains of the Islamic State of Iraq and Syria, a Sunni insurgent group.

June 28, 2014 Members of the all-volunteer Iraq of Imam Hussein Regiment take up positions on a street corner as part of a basic-training course in the Iraqi holy city of Karbala. Shiite men have been ordered by Grand Ayatollah Ali Sistani, the country’s highest Shiite authority, to protect Shiite shrines and help counter the recent gains of the Islamic State of Iraq and Syria, a Sunni insurgent group. Scott Nelson/For The Washington Post

Members of an all-volunteer force undergo training in the holy city of Karbala to protect Shiite shrines and help counter the recent gains of the Sunni insurgent group the Islamic State of Iraq and Syria.

Secretary of State John F. Kerry conferred with Kurdish leaders in northern Iraq as fighters from local Sunni tribes wrested control of at least part of Iraq’s largest oil refinery after battling for days with government troops over the key facility.

Secretary of State John F. Kerry conferred with Kurdish leaders in northern Iraq as fighters from local Sunni tribes wrested control of at least part of Iraq’s largest oil refinery after battling for days with government troops over the key facility.

Syrian government aircraft bombed Sunni militant targets inside Iraq on Tuesday, further broadening the Middle Eastern crisis a day after Israeli warplanes and rockets struck targets inside Syria.

Iraqi state media initially reported that the attacks near Iraq’s western border with Syria were carried out by U.S. drones, a claim that was quickly and forcefully denied by the Pentagon.

Separately, the Pentagon said that 90 additional U.S. troops arrived in Iraq, part of a group of up to 300 military advisers that President Obama said last week he would deploy there to assess the situation before taking any further U.S. military action. A statement said that U.S. aircraft are now flying 30 to 35 manned and unmanned daily surveillance flights over Iraq.

Reuters reported early Wednesday that militants had attacked one of Iraq’s largest air bases, a site near the town of Yathrib that was once know as “Camp Anaconda” when U.S. troops were present. The news agency said the base had been surrounded on three sides and was under mortar fire from the militants.

The main U.S. effort Tuesday was on the diplomatic front, as Secretary of State John F. Kerry traveled to Irbil, the Kurdish regional capital, to urge leaders there to remain part of Iraq. As they met, fighters from local Sunni tribes, apparently working with militant fighters from the Islamic State of Iraq and Syria (ISIS), wrested control of at least part of Iraq’s largest oil refinery from government troops.

“We are facing a new reality and a new Iraq,” Massoud Barzani, president of the semi­autonomous Kurdish government, told Kerry at the start of their meeting.

An independent country is a long-held goal for many in Iraq’s Kurdish minority, numbering about 6.5 million. Some Kurdish leaders see an opportunity in the rapid advance of the insurgents and the slow, disorganized response by the Arab, Shiite-dominated government of Prime Minister Nouri al-Maliki.

Throughout his visit to Iraq, including in talks with Maliki and Sunni leaders Monday in Baghdad, Kerry has argued that Iraq risks collapsing unless a new governing coalition representing all sects and ethnicities is quickly formed.

That argument is harder to make in the Kurdish region, which has several vast oil fields and a long history of at least partial self-rule. The Kurds also have their own defense force, the pesh merga, separate from the Iraqi military that largely melted away in the face of advancing ISIS forces.

This month, as the ISIS militants overran the northwestern city of Mosul and headed south, pesh merga forces quickly secured the oil capital of Kirkuk, which lies just outside the official regional borders but which Kurds have long demanded be included in their territory.

Possible Kurdish secession

U.S. officials traveling with Kerry, who arrived late Tuesday in Brussels for a NATO meeting, said he had raised the question of possible Kurdish secession during his hour-long session with Barzani, but that most of their discussion focused on strategy to form a new Iraqi government.

In an interview, Kerry was asked about Barzani’s “new reality” remark.

“A united Iraq is a stronger Iraq, and our policy is to respect the territorial integrity of Iraq as a whole,” Kerry told NBC. “President Barzani understands that” and will participate in the government formation process, he said. Iraq has until Monday to form a new parliament following elections in April; parliament will then choose a new government.

The United States has long feared that formation of an independent Kurdistan in present-day Iraq would not only weaken Iraq but also set off secession attempts or civil war in neighboring nations with Kurdish minorities.

Meanwhile, Iraqi news media reported that at least 20 people were killed and 93 injured in the strike by Syrian jets in an Iraqi border town controlled by ISIS. Western officials who confirmed the attack said they had no casualty details on the strike, which targeted a market in the town of Qaim, according to the nongovernment National Iraqi News Agency.

On Monday, Israeli warplanes and rockets struck nine targets, including what the Israel Defense Forces said was a Syrian military command headquarters, in retaliation for a missile attack from Syria on Sunday that killed one Israeli and wounded another in the Golan Heights.

ISIS militants are fighting the governments on both sides of the Iraq-Syria border, and an apparent decision by Syrian President Bashar al-Assad to intervene to help Maliki further tangles the already complex knot of actors in the overlapping crises.

In Syria, the United States opposes both Assad and ISIS, which it condemns as a terrorist, al-Qaeda-inspired organization.

Iran supports both Assad and Maliki and is sending aid to both, although Iraq’s ambassador to Tehran on Tuesday denied reports that the leader of Iran’s Revolutionary Guard Corps was in Baghdad helping the government there, Iran’s Fars News Agency reported.

Meeting in Paris

Shiite leaders in Iran and Iraq, as well as Assad, have accused Sunni governments in the Persian Gulf of aiding the militants. On Thursday, Kerry will meet in Paris with his counterparts from Saudi Arabia, the United Arab Emirates and Jordan to ask them to intervene more forcefully with Sunni tribes in western Iraq to sever all ties with ISIS and join efforts to preserve a unified Iraq.

Armed tribal factions apparently worked together with ISIS forces to seize the oil refinery in Baiji, about 140 miles northwest of Baghdad, after days of battles with government troops over the key facility.

There were conflicting accounts late Tuesday of who was in charge at the facility. Iraqi soldiers who arrived in Irbil after fleeing the refinery Monday night said ISIS fighters spearheaded the assault, along with the al-Kaisi tribe that dominates in the region. A tribal council official said Tuesday that “we now control 90 percent of the refinery.”

The Baghdad government insisted it was still in control, but refinery workers said the tribes had negotiated a cease-fire and the surrender of about 450 Iraqi army officers. Some took off their uniforms and put on blue refinery coveralls before leaving, according to the workers’ account, and the tribes arranged for buses to take them away.

According to an official of the Baiji branch of the Military Council of the Revolutionary Tribes, a Sunni self-defense organization that includes the al-Kaisi tribe and other clans in the area, about 50 government troops remain holed up in one part of the refinery.

The official, who gave his name as Khalid al-Iraqi, said tribal fighters were joined by a smaller number of ISIS insurgents in the attack. He said the Military Council controls the refinery and described ISIS as not strong enough in the area to give orders.

But two Iraqi soldiers who took part in the defense, interviewed on the outskirts of Irbil after having fled Baiji, said that ISIS fighters had done most of the attacking.

“This really is a crisis,” said a Western diplomat in Iraq, speaking on the condition of anonymity under ground rules set for a news briefing. “It poses questions as to Iraq’s continued existence as a state. What we’ve got is Sunnis controlling Sunni territory, Shias controlling Shia territory, Kurds controlling Kurdish territory.”

Gearan reported from Irbil and Brussels, Van Heuvelen from Irbil. Abigail Hauslohner in Kirkuk, Iraq, and Loveday Morris and Liz Sly in Baghdad contributed to this report.