ISIS released a video Sunday showing a masked militant standing over the severed head of a man it said was the former U.S. Army Ranger-turned-aid worker, who was seized while delivering relief supplies in Syria last year.
U.S. authorities later confirmed Kassig's death.
"Our hearts are battered, but they will mend," said Paula Kassig, Peter's mother. "The world is broken but it will be healed in the end. And good will prevail as the one god of many names will prevail."
Kassig, who served in the U.S. Army's 75th Ranger Regiment, a special operations unit, deployed to Iraq in 2007. After being medically discharged, he returned to the Middle East in 2012 and formed a relief group, Special Emergency Response and Assistance, to aid Syrian refugees.
A certified EMT, Kassig had delivered food and medical supplies and provided trauma care to wounded Syrians before being captured in eastern Syria on Oct. 1, 2013.
Paula Kassig said her son had witnessed and experienced firsthand more of the harsh realities of life "than most of us can imagine."
"But rather than letting the darkness overwhelm him, he has chosen to believe in the good in himself and others. Peter's life is evidence that he has been right all along. One person makes a difference."
Peter's father asked that people pray this evening at sunset for his son, who reportedly had converted to Islam during his captivity and was going by the name Abdul-Rahman.
"Pray also for all people in Syria, in Iraq and around the world that are held against their will. And lastly, please allow our small family the time and privacy to mourn, cry, and yes, forgive."
Meanwhile, a father in Wales said on Monday he believes his son, a British medical student, was among a squad of ISIS jihadists filmed beheading Syrian soldiers in a video posted online on Sunday.
Ahmed Muthana told the Daily Mail newspaper his 20-year-old son Nasser Muthana appeared to be among a group of 16 jihadists who were seen on the video, which also showed the severed head of Kassig.
"I cannot be certain, but it looks like my son," said Ahmed Muthana, who lives in the Welsh capital city of Cardiff.
"He must fear Allah now for killing people. How can he expect to face Allah if he is killing human beings?"
The announcement of aid worker Kassig's death, the fifth such killing of a Western captive by Islamic State in Iraq and Syria, formed part of the 15-minute video which showed the beheadings of at least 14 men ISIS said were pilots and officers loyal to Syrian President Bashar al-Assad.
ISIS includes thousands of foreign combatants and has become a magnet for jihadi volunteers from Europe and North America, Western intelligence agencies have said.
In Washington, the latest ISIS beheading video has the Obama administration scrutinizing how and why the executioners are unhooded and clearly recognizable, CBC's Lyndsay Duncombe reported. Also new was the lack of specific threats about the next hostage who might die — only a general threat against the U.S., she said.
"[Defence Secretary] Chuck Hagel said yesterday that they will accelerate the training of Iraqi forces to combat ISIS — and that, we know, involves training nine Iraqi security force brigades as well as three pashmerga forces," Duncombe reported.
At the same time, there was debate on Sunday about sending American troops to Iraq.
"What we should have done by now is have American troops standing by in Iraq," said former Republican presidential candidate Mitt Romney. "That's something that we argued for years ago."
Democratic Senator Claire McCaskill of Missouri favoured sticking with the current strategy of getting local forces engaged. "I think we need to give time to this strategy to work," she said.
France's top security official said Monday a Frenchman suspected of joining fighters for ISIS is believed to be among the killers in a video that showed a beheaded American aid worker and a dozen Syrian soldiers.
The British Foreign office declined to comment.
Frenchman seen among beheaders
Interior Minister Bernard Cazeneuve said that there is a "strong presumption" that Frenchman Maxime Hauchard is among the group of Islamic extremist fighters in the video released over the weekend.
Cazeneuve said authorities are analyzing the video and have been investigating Hauchard, who is about 22 and from west of Paris.
French citizens make up the largest contingent of European jihadi fighters who have joined extremists in Syria and Iraq. According to the Paris prosecutor's office, about 1,100 people have been placed under surveillance, and 95 people face charges.
ISIS has previously released videos of the beheading of two American and two British men which feature a masked, black-clad militant brandishing a knife and speaking with an English accent, who has been dubbed "Jihadi John" by British media.
Sunday's video showed most of the killers unmasked, and the Daily Mail said the man who appeared to be Nasser Muthana was standing alongside Jihadi John.
Nasser Muthana had already appeared in a online video released in June urging Muslims to join ISIS.
His younger brother Aseel had also travelled to Syria after both were radicalized in Cardiff, his father told the BBC in June. Nasser Muthana's school friend Reyaad Khan also appeared in the online footage in June, various media reports said.Suggest a correction