Obama vowed that Washington would hunt down the jihadists it held responsible for the 26-year-old aid worker's death, as her family spoke of their heartbreak at losing "a free spirit."
"No matter how long it takes, the United States will find and bring to justice the terrorists who are responsible for Kayla's captivity and death," Obama said in a statement.
Mueller was captured in August 2013 in Aleppo, the war-ravaged city in northern Syria.
IS claimed last week she had been killed in an air strike by a Jordanian warplane in Raqa, the militant group's self-proclaimed "capital," also in Syria, where foreign fighters are flocking at an "unprecedented" rate to join IS and other extremists, US intelligence officials said.
US officials on Tuesday said they remained skeptical of the IS claims Mueller died in an air strike, noting there had been no evidence of civilians at that site before it was targeted.
"That certainly would call into question the claims that are made by ISIL," White House spokesman Josh Earnest said, using an alternate acronym for IS, which has grabbed large areas of Iraq and Syria in a brutal offensive of beheadings and forced religious conversions.
The White House said IS had sent Mueller's distraught family a "private message" that was "authenticated" by intelligence, allowing them to confirm her death. The Washington Post reported that Mueller's parents had been sent a photo of their daughter's lifeless body.
"Our hearts are breaking for our only daughter, but we will continue on in peace, dignity, and love for her," her parents Carl and Marsha Mueller said.
In a letter released by her relatives, Mueller said she took strength during captivity in her faith in God and the love of her family.
"I have been shown in darkness, light + have learned that even in prison, one can be free," said a handwritten letter by Mueller which was smuggled out by fellow captives following their release by Islamic State jihadists
She also revealed times of doubt and darkness, but also resolve as she summoned the will to keep going.
PILOT'S GRUESOME DEATH
Early Tuesday, warplanes from the UAE launched anti-IS air strikes, as the important Arab ally in the US-led coalition against the IS extremists resumed combat operations.
The F-16s hit their targets and returned safely to base, the UAE military said, without saying what their targets were.
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Following the December crash and capture in Syria of Jordanian F-16 pilot Maaz al-Kassasbeh, the UAE withdrew from coalition strike missions, fearing for the safety of its pilots.
The jihadists later killed Kassasbeh by burning him alive, releasing gruesome video footage of his "execution."
The coalition began air strikes against IS in Syria on September 23, but has pointedly refused to coordinate with Damascus.
On Tuesday, the Pentagon said coalition aircraft had launched one strike in eastern Syria in the 24 hours to 0600 GMT, and also pounded the jihadists in Iraq with 11 strikes.
But underlining the scale of the task facing Washington and its allies, the US government's National Counter-Terrorism Center (NCTC) said that about 20,000 volunteers from around the world had bolstered the ranks of the IS or other extremist groups in Syria.
That was up from a previous in January of roughly 19,000, according to NCTC.
'THERE IS NO DIALOGUE'
Syria has grudgingly accepted the air strikes against IS, but has repeatedly criticized the coalition for failing to coordinate with it.
It says the raids cannot defeat IS unless the international community starts cooperating with Syrian troops on the ground.
In an interview broadcast by the BBC, Syrian President Bashar al-Assad confirmed there was no cooperation with the coalition, members of which he accused of backing "terrorism" -- an apparent reference to their support for other rebel groups fighting to overthrow him.
"Sometimes, they convey a message, a general message. There is no dialogue. There's, let's say, information, but not dialogue," Assad said, adding the messages were conveyed via a third party.
In response, the United States denied that it was coordinating air strikes either directly or indirectly with the Syrian regime and renewed calls for Assad to go.
Assad forces have been accused of indiscriminate bombardment of civilians in rebel-held areas, including with barrel bombs -- crude munitions packed with explosives and shrapnel.
But Assad flatly denied the allegation as a "childish story."
"I haven't heard of the army using barrels, or maybe cooking pots," he said, laughing.