The takeover of the Iraqi city of Mosul on Tuesday illustrated an increasingly disconcerting reality for the United States: From Iraq to Syria and beyond, radical offshoots of al-Qaeda are expanding their ambitions and directly threatening American national security interests.

The splinter groups have become a bigger problem than what remains of the old core al-Qaeda, and one that is in many ways harder to address or contain. The loss of Mosul to the Islamic State of Iraq and Syria (ISIS), U.S. officials and experts acknowledged, is a powerful demonstration of the extremists’ growing effectiveness and reach.

Insurgents overran the western bank of the Tigris River in Mosul overnight after U.S.-trained Iraqi soldiers and police officers abandoned their posts. Among the facilities captured were the provincial government headquarters, two prisons, two television stations, numerous police stations, the central bank and the airport, a major military base that used to serve as a hub for U.S. operations in northern Iraq.

ISIS fighters also seized large quantities of weaponry from the security forces when they overran their bases, including vehicles, arms and ammunition, much of it probably supplied by the United States.

Tens of thousands of Iraqi civilians also fled the surprise onslaught.

The Obama administration on Tuesday pledged continued American support for the government of Iraqi Prime Minister Nouri al-Maliki, who announced a “general mobilization” of the country’s security forces and asked parliament to declare a state of emergency. But there are growing concerns about the Iraqis’ ability to stop the Islamist march, even with U.S. advice, weapons and training.

“When a force like that gets momentum and the security forces start to crumble, it becomes difficult to stop,” said a former senior U.S. commander who served in Iraq after the American-led invasion.

The former commander, who like others spoke on the condition of anonymity to assess the situation candidly, said ISIS will consolidate its gains and head south toward Iraq’s capital city. Indeed, several reports Tuesday suggested that insurgents had surrounded Tikrit, which is more than halfway to Baghdad from Mosul.

Even before the latest assault by ISIS, U.S. officials had issued a series of warnings that the group was securing a lasting foothold in the region. Officials said there had been signs that the group considered Mosul, in particular, vulnerable and would try to take it.

“The group looks at Syria and Iraq as one interchangeable battlefield, and its ability to shift resources and personnel across the border has measurably strengthened its position in both theaters,” a U.S. counterterrorism official said.

ISIS has little to no sway outside the Sunni community in Iraq and Syria, but because of its power base in each country, the Obama administration views it increasingly as a regional problem that threatens broader interests.

Michael Vickers, undersecretary of defense for intelligence, said during an appearance at the Center for Strategic and International Studies this month that the Sunni-based group has emerged from the “remnants of al-Qaeda in Iraq.” Instead of being destroyed, he said, the organization appears to have melted away temporarily only to regroup.

“Most of the leadership went to Syria after being significantly degraded in Iraq,” Vickers said. Those leaders now “have ambitions to pose threats broader in the region and outside the region.” He went on to call ISIS “a very malevolent terrorist group and one that we’re increasingly focused on.”

Brett McGurk, a State Department deputy assistant secretary who is a top U.S. adviser for Iraq, was in the country when Mosul, Iraq’s second-largest city, fell. He had gone there for urgent talks about the worsening security conditions in northern and western Iraq, and to press the U.S. argument that Maliki’s Shiite-led government mistreats or marginalizes Sunnis at its peril.

But Mosul’s sudden loss raises questions about the continued utility of sending U.S. military support to Maliki, whose security forces seem simply to have crumbled. Although he is urging the United States to deliver more advanced weaponry, ISIS fighters have been seen riding in U.S.-

supplied Humvees in areas they control, and much of the weaponry captured in this latest battle is likely to be American, said Charles Lister, an Iraq specialist at the Brookings Doha Center.

“Washington will be questioning how to move forward in terms of supporting the Iraqi army,” Lister said. “Every time ISIS captures territory, it’s a reminder that it does so using weapons that have fallen into the hands of the forces the U.S. is trying to counter in the first place.”

Iraq announced plans to buy 18 F-16 aircraft only months after the United States completed its withdrawal of forces in 2011. But Iraq officially took possession of the first plane only this week, and it isn’t expected to arrive there until fall. It will take even longer for Iraq to begin using the planes; only a few pilots are trained to fly them, although more are in training now.

The Iraqi government also is expecting a dozen Apache helicopters from the United States. For months, Senate Foreign Relations Committee Chairman Robert Menendez (D-N.J.) blocked the $6 billion deal over concerns that the Iraqi government could use the Apaches to target minority groups or political rivals. He lifted that hold in January, but even so, the aircraft aren’t expected to arrive in Iraq until this summer.

Washington and Baghdad also struck a $1 billion deal in which light attack planes, surveillance balloons and up-armored Humvees will be delivered to Iraq.

On Tuesday, Rear Adm. John Kirby, the Pentagon’s press secretary, said the United States is monitoring the situation in Iraq closely, but he appeared to shut the door to more U.S. troop involvement.

“This is for the Iraqi security forces and for the Iraqi government to deal with,” he said.

The weaponry deals come as some critics question whether it is wise to continue outfitting the Iraqi military. Iraqi troops were said to have fled their posts in Mosul on Tuesday, and ISIS fighters were seen taking the U.S.-made Humvees they commandeered back over the border into Syria.

The weapons sales follow reports of Iraqis’ use of barrel bombs — crude, cheap explosive devices that can be dropped from helicopters and other aircraft. The Obama administration has been scathing in its criticism of Syrian President Bashar al-Assad for using the same weapons.

In Iraq, barrel bombs have been used to target insurgents, but they lack accuracy and have reportedly killed civilians, especially in Fallujah.

Lukman Faily, Iraq’s ambassador to Washington, said the delivery of the F-16 aircraft was crucial and would allow the Baghdad government to provide needed air support.

“Iraq as a nation, as a state, we need these planes,” he said in a recent interview, conducted before Mosul fell to ISIS.

Faily said Iraq would deal with U.S. concerns about weapons. But he also underscored the threat the Iraqi government faces from ISIS.

“Please bear in mind,” he said, “that we’re in a vicious fight against terrorism.”

Greg Miller in Washington and Liz Sly in Beirut contributed to this report.