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.
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.”
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.