ISIS held Kassig as a hostage and in previous communications had threatened his life.
The video shows the aftermath of a beheading in which the victim is not clearly recognizable.
President Barack Obama confirmed the 26-year-old's beheading, saying Kassig "was taken from us in an act of pure evil by a terrorist group that the world rightly associates with inhumanity."
Kassig, who converted to Islam in captivity, also went by the name Abdul-Rahman Kassig.
He first traveled to the Middle East as a U.S. soldier and returned as a medical worker, feeling compelled to help victims of war.
He did aid work in Syria, where he was captured. He was held hostage for over a year.
"We are heartbroken to learn that our son, Abdul-Rahman Peter Kassig, has lost his life as a result of his love for the Syrian people and his desire to ease their suffering," Kassig's parents, Ed and Paula, said in a statement.
The Kassig family expressed heartbreak over the beheadings of the other Westerners who came before their son, and asked for prayers for the safe return of other captives.
"While ISIL revels in the slaughter of innocents, including Muslims, and is bent only on sowing death and destruction, Abdul-Rahman was a humanitarian who worked to save the lives of Syrians injured and dispossessed by the Syrian conflict," Obama said.
ISIL is another term for the group ISIS, the Islamic State in Iraq and Syria, which calls itself simply the Islamic State.
A familiar figure appeared in Sunday's beheading video, dressed in all black and speaking with what sounds like an English accent.
A man fitting the same description appeared in previous videos of the apparent beheadings of other Westerners.
But this recording is different from previously released ones. It is longer, almost 16 minutes, and does not include a statement by the victim, as previous ones had.
And it is utterly brutal, showing in graphic detail the beheadings of other men, whom militants claim are pilots for the Syrian government.
The narration spends much time on ISIS' history and the figure taunts Obama, saying he will have to return troops to Iraq in greater numbers than before.
And for the first time in such a video, the speaker names the place where he is standing with the victim -- in the town of Dabiq in Aleppo province, Syria.
The fifth Westerner
Kassig is the fifth Westerner whom ISIS claims to have beheaded via video messages.
The first was U.S. journalist James Foley. A video of his killing was posted online in mid-August, just over a week after Obama approved "targeted airstrikes" against ISIS.
In early September, ISIS released a video showing the beheading of U.S. journalist Steven Sotloff. Sotloff's apparent killer spoke in what sounded like the same British accent as the man who purportedly killed Foley.
Less than two weeks later, ISIS announced in a video the apparent killing of British aid worker David Haines.
And on October 3, ISIS released a video showing the apparent beheading of hostage Alan Henning.
Secretary of State John Kerry praised Kassig's compassion and reiterated the goal of defeating ISIS.
"This was a young man who traveled to one of the world's most dangerous places to care for the innocent victims of a bloody conflict, and fearlessly dedicated himself to helping those in need," Kerry said. "There can be no greater contrast than that between Abdul-Rahman's generosity of spirit and the pernicious evil of ISIL."
Plea for mercy
Kassig's life was threatened on the video that showed Henning's killing.
A week after its release, Kassig's family released a YouTube video of their own, asking his captors to show mercy and free him.
Kassig's mother, Paula, addressed her son in the video. "We are so very proud of you and the work you have done to bring humanitarian aid to the Syrian people," she said.
The couple noted they were releasing the video on the day of Islam's Eid al-Adha, or the Festival of Sacrifice, when Muslims slaughter lambs, goats, sheep and cattle and distribute the meat to the poor and their families.
A native of Indiana, Peter Kassig founded Special Emergency Response and Assistance, a nongovernmental organization aiding Syrians fleeing the civil war there.
From 2012, he delivered food and medical supplies within and outside Syria and provided trauma care and training, his family said.
Soldier, helper, captive
Kassig's journey began when he joined the U.S. Army Rangers in 2006 and deployed to Iraq in 2007. He was honorably discharged for medical reasons after a brief tour and returned to the United States to study political science and train for 1,500-meter races. But something wasn't right.
"I was going to school with kids who look the same, were the same age as me, but we weren't the same," he said in an interview with CNN in 2012. "I wanted more of a challenge, a sense of purpose."
In 2010, Kassig took time off and began his certification as an emergency medical technician.
In the two years that followed, he fell in love, got married and quickly divorced. Devastated and heartbroken, he went back to school, but he couldn't shake his depression.
"I needed a game changer," he said.
He eventually traveled to Lebanon and founded SERA to deliver food and medical supplies to swelling refugee camps.
On October 1, 2013, he was "detained" on his way to Deir Ezzor in eastern Syria, his family said.
"Peter really believed that an individual can make a difference in the world through their love and compassion and intelligence," said Margaret Brabant, Kassig's college adviser and a professor at Butler Univeristy in Indianapolis. "... That is the message that I think Peter would want me to convey."
CNN's Alexandra Field, Arwa Damon, Yousuf Basil and Christine Sever contributed to this report.