MARTHA’S VINEYARD, United States/DOHUK, Iraq: President Barack Obama said Thursday that U.S. airstrikes had broken the siege of an Iraqi mountain sheltering civilian refugees and that troops conducting reconnaissance there would be withdrawn.

But he added that U.S. airstrikes would continue against extremists from the Islamic State of Iraq and Greater Syria if they threaten U.S. personnel and facilities in the region, including the Kurdish regional capital Irbil.

“The bottom line is – the situation on the mountain has greatly improved and Americans should be very proud of our efforts because [with] the skill and professionalism of our military and the generosity of our people we broke the ISIS siege of Mount Sinjar,” Obama said in a statement during his vacation in Martha’s Vineyard, Massachusetts.

“We helped save many innocent lives. Because of these efforts, we do not expect there to be an additional operation to evacuate people off the mountain and it’s unlikely we’re going to need to continue humanitarian air drops on the mountain,” Obama said.

Obama, a longtime skeptic of the use of U.S. force in Iraq, last week authorized airstrikes as he warned that thousands of members of the Yezidi community risked “genocide” as they fled to the mountain under pursuit from ISIS extremists.

Obama said that the United States would still carry out airstrikes along with stepping up military assistance to Iraqi government and Kurdish forces battling ISIS.

“We will continue airstrikes to protect our people and facilities in Iraq,” said Obama, who had cited the risk to the US consulate in Irbil as a reason for the military intervention.

Obama, however, said that he still saw a threat to Iraqis, including Christians and Muslims, from ISIS which has vowed to kill anyone who does not share the militants’ hard-line beliefs.

“The situation remains dire for Iraqis subject to ISIS’ terror throughout the country,” Obama said.

Pentagon press secretary Rear Admiral John Kirby had earlier said an American assessment of less than 20 military personnel determined that the number of people still trapped was lower than expected.

“The team has assessed that there are far fewer Yezidis on Mount Sinjar than previously feared, in part because of the success of humanitarian air drops, airstrikes on [ISIS] targets, the efforts of the [Kurdish forces] and the ability of thousands of Yezidis to evacuate from the mountain each night over the last several days,” he said.

“The Yezidis who remain are in better condition than previously believed and continue to have access to the food and water that we have dropped,” Kirby said.

Various countries are ramping up their efforts to aid the trapped civilians and Kurdish forces battling the militants. But even once all civilians have escaped the mountain, major difficulties will remain.

Thousands of people have poured across a border bridge into camps in Iraq’s Kurdish region after trekking through neighboring Syria to find refuge, most with nothing but the clothes on their backs.

Some women carried exhausted children, weeping as they reached the relative safety of the camps.

But the relief of reaching relative safety was tempered by the spartan conditions of the camps hurriedly erected by the Iraqi Kurdish authorities. “We went from hunger in Sinjar to hunger in this camp,” Khodr Hussein said.

As the international outcry over the plight of the Yezidis mounted, Western governments had pledged to step up help for those trapped, and the United Nations declared a Level 3 emergency in Iraq, allowing it to speed up its response.

Obama also reiterated his call for an “inclusive” government, after throwing his support behind Haidar al-Abadi, who has been designated prime minister of Iraq and is seeking to form a government.

“We are urging Iraqis to come together to turn the tide against ISIS above all by seizing the enormous opportunity of forming a new inclusive government under the leadership of the prime minister-designate,” Obama said.

US officials have accused incumbent Iraqi premier Nouri al-Maliki of ruling too divisively on behalf of the country’s Shiite majority.

Abadi, whose nomination was accepted by President Fouad Masoum Monday, has 30 days to build a team that will face the daunting task of defusing sectarian tensions and, in the words of Obama, convincing the Sunni Arab minority that ISIS “is not the only game in town.”

The U.N. Security Council has expressed backing for Abadi’s nomination, calling it “an important step toward the formation of an inclusive government.”

Maliki has defied growing international pressure to step aside and insisted it would take a federal court ruling for him to quit.

In western Iraq, fighting erupted early Thursday in the ISIS-held city of Fallujah, about 65 kilometers west of Baghdad. The clashes on the city’s northern outskirts killed four children, along with a woman and at least 10 militants, said Fallujah hospital director Ahmad Shami.

Meanwhile, eight civilians were killed in separate attacks across Baghdad Thursday.