Iraqi Prime Minister Nouri al-Maliki has rejected forming an emergency government to help the country counter a surge by Sunni Islamist militants.
In a televised address, Maliki said he considered a "national salvation government," intended to present a unified front among Iraq's three main groups, a "coup against the constitution" and going against Iraq's April 30 parliament election results.
Iraqi leaders said they will meet a July 1 deadline for beginning to form the post-election government.
U.S. officials believe the leadership in Baghdad should seek to draw Sunni support away from the militants from the al-Qaida breakaway group the Islamic State of Iraq and the Levant (ISIL).
ISIL militants have seized areas across northern and western Iraq.
U.S. Secretary of State John Kerry, who has been on a week-long tour of the Middle East and Europe to discuss the crisis in Iraq, spoke to reporters at a NATO meeting in Brussels.
Kerry said, "We’ve made it clear to everyone in region that we don't need anything to take place that might exacerbate the sectarian divisions" already occurring in Iraq.
He also said the U.S. is interested in who leads Iraq but is not going to interfere as Baghdad forms a new government.
"It's up to Iraqis to make those decisions. We have stated clearly that we have an interest in a government that can unite Iraqis," Kerry said.
Both Kerry and U.S. President Barack Obama have been urging Iraq to install a government that is inclusive of Iraq's Sunni and Kurdish minorities.
On Friday, Kerry will visit Saudi Arabia on Friday to meet King Abdullah and discuss the crises in Iraq and Syria, he said at a news conference in Brussels on Wednesday.
Kerry last visited the world's top oil exporter in late March alongside U.S. President Barack Obama. He will most likely meet the Saudi monarch in Jeddah, where the kingdom's government is based during summer months.
The United States and Saudi Arabia have both been alarmed by the success of ISIL.
However, officials from Saudi Arabia, which has long complained that Iraq's Sunnis are marginalized by Maliki, said they oppose foreign intervention in Iraq after Baghdad requested U.S. air strikes on ISIL.
Call to unite
Maliki's Shi'ite-led government has faced criticism of sidelining the minorities and breeding sectarian tensions. He called for unity in his address Wednesday.
"We desperately need to take a comprehensive national stand to defeat terrorism, which is seeking to destroy our gains of democracy and freedom, set our differences aside and join efforts," Maliki said. "The danger facing Iraq requires all political groups to reconcile on the basis and principles of our constitutional democracy."
Middle East analyst Nadim Shehadi of Chatham House in London argued many in the West are making too much of the role of ISIL militants in the battle against the Maliki government.
"There is too much concentration on ISIL and the militants. There is a lot more to that than ISIL and the militants," Shehadi said. "Underneath that is a genuine discontent and marginalization on the part of mainly Sunni constituency and one should not address ISIL as being the main protagonist. It affects the solution. It affects the way you seek a solution."
Shehadi went on to stress that “underlying discontent” among Sunni tribes is what sparked the revolt against the Maliki government.
“ISIL,” he insisted, “jumped in to take advantage of the rift or discontent.” The “solution” to the conflict, he claimed, “is to address the discontent, not to address ISIL.”
Oil refinery, air base attacked
On Wednesday, militants overran the Ajeel oil site, 30 kilometers (19 miles) east of Tikrit, which contains at least three small oil fields that produce 28,000 barrels per day, an engineer working at the field said.
The engineer said local tribes had taken responsibility for protecting the fields after police withdrew but that they also left after the nearby town of al-Alam was seized by militants.
Ajeel is connected to two pipelines, one running to Turkey's Ceyhan port and the other to the Beiji oil refinery, which remained a frontline early on Wednesday.
State TV showed troop reinforcements flying into the compound by helicopter to fend off the assault on Beiji, a strategic industrial complex 200 kilometers north of Baghdad.
Local tribal leaders said they were negotiating with both the Shi'ite-led government and Sunni fighters to allow the tribes to run the plant if Iraqi forces withdraw.
One government official said Baghdad wanted the tribes to break with ISIL 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 no clear winner so far.
Militants including ISIL and allied Sunni tribes battled Iraqi forces in the town of Yathrib, 90 km north of Baghdad, into the early hours of Wednesday, witnesses and the deputy head of the municipality said. Four militants were killed, they said.
Insurgents have partially surrounded a massive air base nearby Balad, which was known as "Camp Anaconda" under U.S. occupation, and struck it with mortars.
The loss of Balad would be a powerful blow to the Shi'ite-led government of Maliki and could threaten the capital from the air. It could also pave the way for a Sunni insurgent assault on a second major air base at Taji.
Images from Iraq
A Shi'ite volunteer who joined the Iraqi army to fight against predominantly Sunni militants from the radical Islamic State of Iraq and the Levant looks on during a parade in Kanaan, Iraq, June 26, 2014.
Shi'ite volunteers who joined the Iraqi army to fight against predominantly Sunni militants from the radical Islamic State of Iraq and the Levant take part in a parade in Kanaan, Iraq, June 26, 2014.
Fleeing Iraqi citizens from Mosul and other northern towns sit in a pick up truck between Mosul and Irbil, northern Iraq, June 25, 2014.
An Iraqi woman who fled her village holds her daughter near a Kurdish checkpoint, in the Khazer area between Mosul and Irbil, northern Iraq, June 26, 2014.
Members of the Iraqi security forces take their positions during an intensive security deployment west of Baghdad, June 24, 2014.
Members of Iraqi security forces take their positions along a road during an intensive security deployment west of Baghdad, June 24, 2014.
A military convoy drives towards Kirkuk, to reinforce Kurdish Peshmerga troops, Iraq, June 24, 2014.
Kurdish regional President Massoud Barzani listens to U.S. Secretary of State John Kerry during a meeting at the presidential palace in Irbil, Iraq, June 24, 2014.
Kurdish security forces take their positions at a checkpoint on a highway between the Iraqi city of Mosul and the Kurdish city of Irbil, in Khazer, northern Iraq, June 24, 2014.
U.S. Secretary of State John Kerry meets with Iraqi Prime Minister Nouri al-Maliki in Baghdad, June 23, 2014.
U.S. Secretary of State John Kerry speaks with Sayyed Amar Al-Hakim, head of Supreme Islamic Council, during a meeting in Baghdad, June 23, 2014.
A fighter with the Islamic State of Iraq and the Levant distributes a copy of the Quran, Islam's holy book, to a driver in central northern city of Mosul, Iraq, June 22, 2014.
US forces arrive
The attack came as the first of up to 300 U.S. military adviser, meant to help Iraq counter the militants, arrived in Baghdad to assess the government's military position.
More than 100 security personnel arrived earlier this week and more are scheduled to arrive in the next few days.
The United States also is conducting air surveillance over Iraq, with 30 to 35 flights a day to help gain better insight about the security situation on the ground as Iraqi troops battle the fast-moving insurgency.
The United Nations said Tuesday that more than 1,000 people have been killed in Iraq in June, most of them civilians. Iraq is seeing its worst violence since 2008, with U.N. figures showing 4,500 deaths through the end of May.
Edward Yeranian contributed to this report from Cairo. Some information for this report provided by Reuters and AP.