BEIRUT (AFP) - US President Barack Obama has ordered a review of how Washington can release American hostages, as intelligence agencies investigated the involvement of Western militants in the beheading of aid worker Peter Kassig.

The announcement of the review came just 24 hours after the release of a video by the Islamic State in Iraq and Syria (ISIS) claiming the beheading of Kassig.

He was the third American to be killed by ISIS, following the deaths of journalists James Foley and Steven Sotloff.

On Monday, the parents of the 26-year-old Mr Kassig paid tribute to their son and said they would try to "forgive" the militants.

In the letter from Mr Obama, dated last Tuesday, Ms Christine Wormuth, the US undersecretary of defence for policy, said the review will focus "on examining family engagement, intelligence collection and diplomatic engagement policies".

"The president recently directed a comprehensive review of the US government policy on overseas terrorist-related hostage cases," Ms Wormuth said in the note posted on The Daily Beast news site.

The move, she said, comes "as a result of the increased frequency of hostage-taking of Americans overseas, and the recognition of the dynamic threat posed by specific terrorist groups".

The killing of Kassig and the simultaneous beheadings of at least 18 Syrian military personnel in the video sparked global horror, with Mr Obama calling it "an act of pure evil".

Mr Kassig's parents on Monday called for healing and prayer as they mourned their loss.

"Please allow our small family the time and privacy to mourn, cry and - yes - forgive and begin to heal," Mr Kassig's father, Mr Ed Kassig, said in an emotional address outside his church.

"Please pray for Abdul-Rahman, or Pete if that's how you knew him, at sunset this evening. Pray also for all people in Syria, in Iraq and around the world that are held against their will."

His mother, Mrs Paula Kassig, said that while their world had been torn apart by the death of their son, they would focus on healing.

"Rather than letting the darkness overwhelm him, he has chosen to believe in the good, in himself and in others... One person makes a difference," she said.

"Our hearts are battered. But they will mend. The world is broken, but it will be healed in the end." In Mr Kassig's home state of Indiana, Governor Mike Pence called the killing "an unspeakable act of barbarism".

US Secretary of State John Kerry also used the word "barbarism" to describe ISIS on Monday, insisting the world would not be intimidated in the battle against it.

It was the latest in a series of atrocities by ISIS, a Sunni Muslim extremist group that has seized control of large parts of Iraq and Syria.

The video showed the Syrian men kneeling on the ground each before a separate executioner, whose faces were uncovered.

Among the militants shown beheading the Syrian servicemen were some known foreign fighters, including at least one Frenchman and possibly a Briton, an Australian and a Dane.

French authorities identified one of the executioners as Maxime Hauchard, a 22-year-old from a small village in northern France who left for Syria in August last year.

The Paris prosecutor's office said "circumstantial evidence confirms the involvement of a Frenchman in the decapitation of Syrian prisoners shown in an ISIS video released on Sunday".

It added it was "possible" a second Frenchmen appeared in the video but said it was yet to confirm the individual's identity.

Thousands of foreign fighters have flocked to join ISIS in Iraq and Syria, and experts say they are often among the most violent and brutal of the jihadists.

A British-accented militant has been at the centre of previous beheading videos and appeared again in Sunday's recording claiming Mr Kassig's killing.

The father of another British militant fighting with ISIS initially told the media he had also seen his son in the video, but later said he was mistaken.

Mr Kassig, who took the name Abdul-Rahman after converting to Islam, was captured last year and became the fifth Western hostage beheaded by IS after the two US reporters and two British aid workers.

In the undated video released on Sunday, the militant stands above a severed head he claims is Kassig's and challenges Obama to send more troops to the region to confront IS.

"Here we are burying the first American crusader in Dabiq, eagerly waiting for the remainder of your armies to arrive," the militant says, referring to a northern Syrian town.

Washington is preparing to double its military personnel in Iraq to up to 3,100 as part of the international campaign it is leading against the jihadists.

Mr Kassig, an Iraq war veteran, had risked his life to provide medical treatment and relief supplies to those suffering from Syria's civil war.

Sunday's video was substantially different from previous ISIS recordings of beheadings.

Mr Kassig was not shown alive in the footage, and no direct threats were made against other Western hostages.

The video came as ISIS suffered battleground setbacks in Iraq supported by US-led air strikes, with government forces Saturday breaking the militants' months-long siege of the country's largest oil refinery.

Monitoring group the Syrian Observatory for Human Rights said it had documented the execution of 1,429 people in Syria by ISIS in the five months since it declared the establishment of a "caliphate" in areas under its control.