Barack Obama, claiming victory for the United States in ending the Islamic State (Isis) siege of thousands of Iraqis atop Mount Sinjar, indicated that the US and UK militaries will no longer drop food, water and medicine to beleaguered Yazidis.

“It’s unlikely that we are going to need to continue humanitarian airdrops on the mountain,” Obama said in a brief appearance before reporters on Thursday.

A dramatic operation on Wednesday placed a handful of US special operations forces and aid workers on a reconnaissance mission atop the mountain deep inside Isis-plagued Iraq, where the US had feared a genocide would unfold.

Yet the Pentagon announced on Wednesday night that there was no longer any need for a risky rescue effort, as days’ worth of US air strikes and Kurdish-led exfiltration efforts had permitted most of the Yazidis chased up the mountain to escape.

“Because of the skill and professionalism of our military, and the generosity of our efforts, we broke the [Isis] siege of Mount Sinjar, we helped vulnerable people reach safety, and we helped save many innocent lives,” Obama said.

The reinforcement complement of US advisers, who Obama sent sent this week to Irbil and who helped with the reconnaissance effort, will leave Iraq in the coming days, he said. Their arrival stirred great speculation that the US was “Americanizing” the latest Iraq war by degree.

While the administration had said that the latest wave of US air strikes in Iraq was prompted by the need to provide relief to Mount Sinjar’s Yazidis, Obama also indicated the US is not ready to end its resumed military involvement.

“We will continue air strikes to protect our people and facilities in Iraq. We have increased the delivery of US military assistance to Iraqi and Kurdish forces fighting [Isis] on the frontlines,” Obama said.

Separately, Rear Adm. John Kirby, the Pentagon press secretary, said the Pentagon believes approximately 4,000 to 5,000 Yazidis remain atop the mountain, with perhaps up to 2,000 of them residents of the area who might not desire to leave.

Kirby credited US air strikes and Kurdish peshmerga forces that accompanied Yazidis off the mountain.

While earlier assessments had placed the number of Yazidis on Mount Sinjar in the tens of thousands, Kirby resisted assertions that US intelligence, aided by nearly 60 daily surveillance flights over Iraq, had miscast the situation.

“It’s very difficult to do nose counts from the air,” he said.

Humanitarian aid workers in northern Iraq have yet to provide an independent assessment of Mount Sinjar.

“There are still thousands on the mountain who continue to suffer, and our thoughts and prayers go out to those that have lost their lives, lost loved ones, been hurt, been injured, either by [Isis] or in the passage off the mountain, but the fact is, most of them have left, and most of them have found shelter or sustenance elsewhere,” Kirby said.

The United Nations has declared its highest level of emergency for civilians in Iraq, thanks to Isis’s two-month-long campaign, and Obama said the US would look to work with allies to “provide humanitarian assistance to those suffering in northern Iraq wherever we have capabilities and wherever we can carry out effective missions like the one we carried out on Mount Sinjar, without committing combat troops on the ground”.

The military is “certainly going to hold that option open”, Kirby said, although the initial rationale given by Obama last week for the humanitarian end of the intervention concerned the Yazidis, not Iraqis in general at the mercy of Isis.

“The threat that [Isis] poses is not over. It’s not like we’re just breathing a sigh of relief now just because things look to be better on Mount Sinjar,” he said.