WASHINGTON — President Obama took credit today for liberating Yazidis cornered by the Islamic State on Mount Sinjar while the Pentagon acknowledged that they’re not doing a “happy dance” over the members of the persecuted minority still suffering in the inhospitable environment.

From his vacation spot in Massachusetts, Obama declared a mission accomplished of sorts for the military and humanitarian action he approved a week ago.

“We also knew that ISIL terrorists were killing and enslaving Yazidi civilians in their custody and laying siege to the mountain,” Obama said. “Without food or water, they faced a terrible choice: starve on the mountain or be slaughtered on the ground. That’s when America came to help.”

“Because of the skill and professionalism of our military and the generosity of our people, we broke the ISIL siege of Mount Sinjar, we helped vulnerable people reach safety, and we helped save many innocent lives,” he continued. “Because of these efforts, we do not expect there to be an additional operation to evacuate people off the mountain. And it’s unlikely that we’re going to need to continue humanitarian air drops on the mountain. The majority of the military personnel who conducted the assessment will be leaving Iraq in the coming days.”

Obama acknowledged “the situation remains dire for Iraqis subject to ISIL’s terror throughout the country.”

“And this includes minorities like Yazidis and Iraqi Christians. It also includes many Sunnis, Shia, and Kurds,” he said. “…We obviously feel a great urge to provide some humanitarian relief to the situation, and I’ve been very encouraged by the interest of our international partners in helping on these kinds of efforts as well. We will continue air strikes to protect our people and facilities in Iraq.”

Kurdish news agency Rudaw reported today that the danger on the mountain is far from over, even though the Peshmerga opened a route for Yazidis to flee. One mother told the news agency how ISIS terrorists raped her three daughters, then sent them up to join their family — where the anguished girls committed suicide by leaping from Mount Sinjar.

“Another Halabja is happening to us,” a woman praying for death told a reporter, referencing the gassing of the Kurds by Saddam Hussein. “We are disabled, we can’t walk anymore. No food, no water, our children have all died.”

At the Pentagon today, press secretary Rear Adm. John Kirby said Defense Secretary Chuck Hagel was “very proud that we’ve been able to effect this kind of change around Mount Sinjar.”

It was the assessment of a small team that there weren’t as many Yazidis as previously thought on the mountain and some pallets of supplies had been untouched, leading the administration to drop any plans for evacuation efforts.

Kirby said about half of the 25 airstrikes conducted thus far have been to “hit ISIL targets in and around Erbil with respect to the protection of U.S. personnel and facilities” — and those strikes “put a hurting on” ISIS — and the other half were around Mount Sinjar.

“On the estimate of refugees on Mount Sinjar, it’s difficult to provide an exact figure, but we think it’s somewhere between 4,000 and 5,000. I’d also add that a number of them, perhaps up to 2,000 or so — and, again, this is an estimate — reside there and may not want to leave. It’s home to many of them. So not all of them will necessarily be looking to leave the mountain,” he said. “That’s our best estimate right now, based on the assessment team’s visit there.”

Kirby said they do believe “there were tens of thousands of Yazidis on that mountain,” but “certainly more than 1,000 or so every night were leaving the mountain with Peshmerga help, again, because of the security and the sustenance that we provided.”

“I think it’d be difficult and imprudent to think that we could know everything simply by flying over a mountain even 24/7. So we made the best estimates we could based on the limited picture we had from the air,” he said, adding that Hagel sent the “less than” 20-member assessment team to the mountain “because there’s no substitute for getting eyes on.”