The deepening rift between Sunni nations and Iran is putting growing pressure on the Obama administration to reassure Middle East allies who feel "abandoned" over Washington's diplomatic outreach to Tehran.  

The split widened Monday as Bahrain and the UAE joined Saudi Arabia in either cutting off or downgrading ties with Tehran. The diplomatic crisis erupted after Saudi Arabia went forward with a mass execution which included the killing of a prominent Shia cleric, and Iranians retaliated by storming the Saudi embassy in Tehran. 

Saudi Arabia's response, though, reflected not only its outrage at Iran but an undercurrent of frustration with the United States’ reluctance to hold Iran accountable for alleged aggressions. One Saudi official was quoted complaining that the U.S. "backs off" every time Tehran crosses a line. 

Among other moves, a recent decision by the U.S. to delay sanctions against Tehran could be inflaming that frustration -- and in turn making it more difficult for Washington to help resolve the dispute. 

For now, the administration is treading carefully and showing little interest in diving into the middle of the fight. State Department spokesman John Kirby said he doesn’t believe the U.S. should act as a “mediator” between the two sides. 

But Robert Jordan, former U.S. ambassador to Saudi Arabia from 2001-2003, told FoxNews.com the Saudis and their allies “feel abandoned by the United States” and urged the U.S. to get more involved.  

“The backdrop of animosity and of proxy wars has been getting more dramatic,” Jordan said. “We need to make it clear that we’re not simply singing ‘Kumbayah’ with Iran and that we still see them as a revolutionary state.” 

White House Press Secretary Josh Earnest on Monday pushed back strongly on accusations the U.S. was looking the other way with Iran. He added that sanctions are still on the table but also warned Saudi Arabia wasn’t getting a free pass from the U.S. on its mass executions.

“We’re urging all sides to show restraint, not further tensions,” he said at the daily briefing.

On Sunday, Saudi Arabia cut diplomatic ties with Iran and gave Iranian diplomats living in the country only hours to flee. The move highlighted a stunning escalation in the decades-old bad blood between the two nations.

Saudi Foreign Minister Adel al-Jubeir made the announcement after Iranian leaders sharply criticized Saudi Arabia for executing outspoken Shiite cleric Sheikh Nimr al-Nimr, among a group of 47 executed. Protesters in Iran stormed the Saudi Embassy in response to the killings.

“The killings – the beheading -- was nothing more than a spark that ignited what had been simmering,” Professor Alon Ben-Meir, a senior fellow at New York University’s Center for Global Affairs and senior fellow at the World Policy Institute, told FoxNews.com.

The fracture in ties comes at a time when the United States and other Western countries had hoped civility between the two Middle Eastern nations would ease tensions in Iraq, Bahrain and other political hotspots in the region. 

But instead of staying out of the fight, three Sunni-led countries – Bahrain, Sudan and the United Arab Emirates -- joined Saudi Arabia’s lead on Monday. 

Bahrain accused Iran of spreading “devastation and destruction” around the world and provoking “unrest and strife in the region.”

Sudan -- which is not a U.S. ally and, like Iran, is considered a state sponsor of terrorism -- kicked out its Iranian ambassador, while the UAE downgraded its ties to Tehran by ordering a reduction in the number of Iranian diplomats stationed in the UAE.

For its part, U.S. officials have been working to ease the tensions.

The White House said Secretary of State John Kerry spoke with Iranian Foreign Minister Mohammad Javad Zarif on Sunday, while the Saudi Press Agency reported that Kerry had also spoken with Saudi Deputy Crown Prince Salman. The Associated Press said that Kerry would likely make another round of calls to the foreign ministers of all the Sunni-led states in the region, including Bahrain, UAE, Kuwait and Qatar.

Several officials said one of Washington's most immediate concerns is the potential effect the spat could have on the fragile cooperation in Iraq between the Iraqi security forces, which answer to an Iran-friendly government, and Sunni and Shiite militias that are fighting Islamic State extremists. That cooperation has shown gains in recent weeks, notably with the Iraqi recapture of the provincial capital of Ramadi from the Islamic State group.

Officials were preparing for a high-level U.S. conversation with Iraqi Prime Minister Haider al-Abadi to stress the importance of continuing the Iraqi government's outreach to Sunni militias, the officials said.

Also of concern is the state of the Syrian peace effort, which is supposed to swing into high gear in late January with U.N.-sponsored negotiations between Saudi-backed opposition forces and the Iranian-supported government of Syrian President Bashar Assad. 

In addition to Kerry, other senior U.S. diplomats were in close contact with Saudi and Arab officials over the weekend, according to U.S. officials. 

But at least one U.S. official blamed the Saudi government for stoking tensions by executing al-Nimr, who was a central figure in Arab Spring-inspired protests by Saudi Arabia’s Shiite minority until his arrest in 2012.

"This is a dangerous game (the Saudis) are playing," the official told The Washington Post. "There are larger repercussions than just the reaction to these executions."

That drew an angry response from a Saudi official, who also told the Post, "Tehran has thumbed its nose at the West again and again, continuing to sponsor terrorism and launch ballistic missiles and no one is doing anything about it."

"Every time the Iranians do something, the United States backs off," the official added, according to the Post. "The Saudis are actually doing something."

During his daily briefing, Earnest warned that the U.S. would not be pressured by any country into enforcing economic sanctions against Iran.

“We know those kinds of financial penalties have an impact and they are helpful in countering Iran’s ballistic missile program but ultimately we will impose those financial penalties, we’ll impose those sanctions at a place of our choosing, when our experts believe they will have the maximum impact and those decisions are not subject to negotiation by the Iranians or by anybody else for that matter,” Earnest said. “Those decisions are made based solely on the conclusion of our financial experts about ensuring those penalties have the maximum impact.” 

FoxNews.com's Barnini Chakraborty and The Associated Press contributed to this report.