BEIRUT — American military officials said Thursday that U.S. and allied airstrikes had crippled most of the small oil refineries controlled by Islamic State in Syria, and the remainder would be targeted in coming days.

“The point was to render them incapable of using these refineries, which was a significant stream of revenue for them,” Rear Adm. John Kirby, the Pentagon press secretary, told reporters Thursday.

The attacks by the U.S. military and two Arab partners were part of a broadening assault on Islamic State in Syria and Iraq. Britain was expected to join the coalition with a parliamentary vote on Friday approving airstrikes in Iraq.

But despite the stepped-up effort, the radical Islamist fighters are threatening to expand their grip on Syria by trying to take a key town on the Turkish border. Kurdish Syrian leaders appealed Thursday for American warplanes to help them by hitting Islamic State units near the town of Kobane, known as Ayn al-Arab in Arabic.

The Obama administration is seeking to assemble an international coalition to destroy Islamic State, an al-Qaida offshoot also known as ISIS or ISIL. The group has seized control of a large swath of land crossing the Syrian-Iraqi border and is seeking to impose a caliphate, or nation ruled by a strict version of Islamic law.

Kirby said the Islamic State produced about 300 to 500 barrels a day from each of the small refineries in Syria, providing the jihadists with revenue as well as refined fuel for their vehicles.

He told reporters in Washington that U.S. military officials were still conducting damage assessments from the attacks a day earlier, but were confident that the dozen facilities that were targeted had been disabled. The warplanes tried to partially damage the refineries with precision-guided munitions instead of destroying them, he added. Some of the infrastructure was left intact in the hope that a future Syrian government – controlled by moderate forces instead of President Bashar Assad or the Islamic State – might be able to restart the refineries, he said.

While the attacks marked an expansion of the new offensive in Syria, the Islamic State makes most of its money from crude oil, not refined. So the latest airstrikes will not be enough to shut down the flow of Islamic State oil, analysts said.

“The air strikes on the oil refineries were tactically spectacular, but strategically insignificant,” said Chris Harmer, a senior analyst with the Washington-based Institute for the Study of War who previously served with the U.S. military in Iraq and Bahrain.

“ISIS controls the oil fields. Destroying small oil refineries will just shift production from small refineries controlled by ISIS to micro refineries located in residential neighborhoods,” he said.

The Pentagon emphasized that the operation was led by fighter jets from Saudi Arabia and the United Arab Emirates, with U.S. warplanes dropping fewer than half of the bombs. The Obama administration has sought to emphasize the participation of Arab militaries in the airstrikes, in part to deflect the charge that the United States is waging a war on Muslims.

In northern Syria, Kurdish fighters said Islamic State forces were battling to advance on Kobane. The Kurdish town’s fall would give the militants control over an important stretch of the Syrian-Turkish frontier. More than 130,000 people have fled during about 10 days of clashes in the border area.

Syrian opposition activists reported airstrikes in the area on Wednesday, but the U.S. military has not confirmed any activity there.

“The strikes have shown no effect on the ground and resistance is very difficult,” said Abdul Azzizi, a Kurdish activist from Kobane who has moved to near the Turkish border.

Kurdish Syrian leaders pleaded again Thursday for American assistance.

“(The) bases of ISIL and all their heavy weapons, vehicles and equipment are in the open air, visible to everyone, but yet they haven’t been targeted by the airstrikes,” said a statement from Redur Xelil, spokesperson of the People’s Protection Units, one of the Kurdish groups.

Across the border in Iraq, U.S. planes carried out airstrikes ranging from near the northern city of Irbil to areas west of Baghdad, targeting fighters and vehicles including a tank, according to a Central Command statement.

France, which last week launched its first airstrikes in northern Iraq, followed up Thursday with more attacks, French media reported. The airstrikes came a day after a French citizen, Herve Gourdel, was beheaded by an Algerian Islamist group claiming revenge for French military action against the Islamic State.

In a possible gain for Assad, meanwhile, government forces took control of an Islamic State foothold in an area about 19 miles northeast of Damascus, according to Hezbollah’s Al-Manar TV. The report could not be independently verified, but Lebanon-based Hezbollah has helped support Assad by sending fighters to Syria.