WASHINGTON >> A remarkable clash between two key U.S. allies in the Middle East burst into the open here on Wednesday as the Iraqi prime minister publicly criticized the Saudi air campaign in Yemen and a top Saudi official retorted that there was “no logic to those remarks.”

The exchange, driven by sharply opposing views of Iran in the region, reflected the challenges facing the Obama administration as it tries to hold together a diverse coalition, including Sunni Arab states and Shiite-dominated Iraq, in the fight against the Islamic State. Iran is a sometimes patron to Iraq but an ideological archrival to Saudi Arabia.

The United States remains caught in a difficult balancing act as it tries to keep the Saudi air campaign in Yemen on track against Iranian-backed Houthis. But in its fight against the Islamic State in Iraq, the Obama administration finds itself supporting an Iraqi military offensive that is also backed by Iran.

The dueling Iraqi and Saudi narratives began when Prime Minister Haider al-Abadi of Iraq, who this week is making his first official visit to Washington, spoke early in the day to a small group of reporters at Blair House, the White House guest residence for visiting dignitaries. He said the Saudi campaign and the fighting in Yemen had created huge humanitarian problems.

“There is no logic to the operation at all in the first place,” al-Abadi said. “Mainly, the problem of Yemen is within Yemen.”

Al-Abadi, who is in Washington seeking U.S. military help in the fight against the Islamic State as well as billions of dollars to shore up his sagging economy, then suggested that the Obama administration agreed with him in his concerns about the Saudi campaign.

“They want to stop this conflict as soon as possible,” al-Abadi said. “What I understand from the administration, the Saudis are not helpful on this. They don’t want a cease-fire now.”

The administration swiftly denied that President Barack Obama had expressed concern about the Saudi air campaign during a meeting with al-Abadi on Tuesday at the White House.

“The president did not criticize Saudi or GCC actions in Yemen,” said Alistair Baskey, a spokesman for the National Security Council, using the acronym for the Gulf Cooperation Council.

At the same time, Baskey said, Obama had conveyed his view to the Iraqi prime minister “that this not escalate into a broader conflict and that ultimately Yemen’s conflict can only be settled through a political negotiation.”

In his remarks to reporters, al-Abadi also said he was worried that Saudi airstrikes might be a precursor for a more assertive Saudi military role in neighboring states.

“The dangerous thing is we don’t know what the Saudis want to do after this,” al-Abadi said. “Is Iraq within their radar? That’s very, very dangerous. The idea that you intervene in another state unprovoked just for regional ambition is wrong. Saddam has done it before. See what it has done to the country.”

A few hours later Adel al-Jubeir, the Saudi ambassador to Washington, held a news conference at the Saudi Embassy and made his remarks about al-Abadi in response to questions from reporters, some of whom had met with al-Abadi at Blair House.

In addition to saying that there was “no logic” to al-Abadi’s remarks, al-Jubeir set forth a highly positive picture of the Saudi campaign in Yemen. He said that the bombing had destroyed attack planes, helicopters, ballistic missiles, air defenses and command elements. But he gave no precise figures.

Saudi officials have insisted that their airstrikes, which they named Operation Decisive Storm, have been effective in weakening the Houthi forces.

Al-Jubeir rejected as “false” reports that Saudi bombers had accidentally killed numerous civilians in some of their airstrikes, and said Saudi Arabia had taken measures to minimize risks to Yemeni civilians.

The air campaign has also created fissures among the Houthi and loyalists to the former Yemeni president, Ali Abdullah Saleh. Al-Jubeir said the bombing had prompted some senior Yemeni officers — he did not say how many — to abandon Saleh.

“We’re beginning to see cracks in their leadership,” al-Jubeir said.

The ambassador dismissed al-Abadi’s claim that U.S. officials were worried about the goals and conduct of the air campaign, saying that no American official had complained to him about it.

The United States is flying Predator and Reaper reconnaissance drones over Yemen, and transmitting the information to a 20-person U.S. military coordination team divided among Saudi Arabia, Qatar and Bahrain, overseen by Maj. Gen. Carl E. Mundy III, the deputy commander of Marines in the Middle East, said a senior U.S. military official who wanted to remain anonymous because he was discussing targeting procedures.

Under the arrangement, Saudi Arabia gives lists of potential targets to the U.S. analysts for vetting. “We are not choosing their targets, but upon request, we’re providing intelligence to help Saudi Arabia with their precision, effectiveness and avoidance of collateral damage,” the official said.

In other comments to reporters, al-Abadi played down Iran’s role in military operations in his own country — he said that Iran had only 110 military advisers in Iraq, far fewer than U.S. military estimates. And he said that Iran’s role was understandable because some of the Islamic State attacks in Iraq were near Iran.

James F. Jeffrey, a former U.S. ambassador to Baghdad, said that al-Abadi’s remarks reflected deep-seated Iraqi concerns that sectarian tensions in the region might escalate further with devastating consequences for Iraq.

“The underlying fear in the whole Middle East given the weak state system in most countries is this three-way tug of war between Iran, Sunni Arab state and the Sunni Islamist militant movements,” Jeffrey said.

“The Iraqis are openly angry with the Saudis and they are almost certainly quietly unhappy with the Iranians,” he added. “They would be the first victims of a Sunni-Shia cataclysm and don’t want to be a bigger version of Lebanon.”

Later on Wednesday, Iraq’s oil minister, Adel Abdul Mahdi, told reporters that the Islamic State had seized control of some of the towers surrounding the Baiji oil refinery in northern Iraq last Friday and had infiltrated part of the complex. The Islamic State militants, he said, are trying to mount a counterattack after their recent loss of the city of Tikrit. Mahdi said he was confident that the militants would eventually be defeated.

Also on Wednesday, Iraq’s finance minister, Hoshyar Zebari, said that Iraq is planning to issue $5 billion in bonds to try to cover a large budget deficit, which he said was about $25 billion for 2015. Iraqi officials have been in negotiation with Citibank and Deutsche Bank, which would underwrite the bonds.

Iraq is also hoping to receive about $400 million to $700 million from the International Monetary Fund, though the fund has been insisting that the country do more to cut public spending as a condition of receiving the funds, Zebari said. Iraq is also hoping to work out an arrangement with the Export-Import Bank of the United States to finance the purchase of Boeing commercial aircraft, which would provide Iraq with $500 million in short-term funds.

It has taken other steps to try to ease its budget squeeze, including $4.2 billion in reparations to Kuwait for Saddam Hussein’s 1990 invasion of the country.

Al-Abadi said that the next step in military operations against Islamic State fighters was to try to roll them back in Iraq’s western Anbar province and north of Baghdad, toward the oil refinery at Baiji. A military push to retake the northern city of Mosul, he said, would not occur before Ramadan, which begins in mid-June.

On Wednesday, the Islamic State launched a major offensive in Anbar, and by the end of the day had captured three villages on the outskirts of Ramadi, the provincial capital, officials said.

During the fighting, hundreds of people from the besieged villages fled their homes, many ending up in Ramadi. State television reported Wednesday that the Islamic State was burning homes and massacring civilians in the areas it had seized, although those reports could not be independently verified.

Anbar officials said that the army had fled the villages that were under attack, leaving tribal fighters and the local police, who they said were badly outgunned by the militants, to defend the areas.

In recent days the U.S.-led coalition struck several Islamic State targets near Ramadi, according to a Pentagon statement.

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