"I need to know that I've done everything I can"

American Peter Kassig, who adopted the first name of Abdul Rahman in captivity, has been held by the Islamic State of Iraq and Syria (ISIS) for over a year.

For most of that year, parents Ed and Paula Kassig kept their son's abduction a secret -- an order from his captors.

But after ISIS threatened to kill Peter in the terror group's latest execution video, the Kassig family decided to go public.

"We're doing everything we can to secure his release," Ed told CBS News correspondent Margaret Brennan in the couple's first television interview.

"We couldn't answer honestly when people would ask us. So we had to lie to our friends again and again and again," Paula said.

But the recent murder of American journalist Steven Sotloff, Kassig's cellmate at one point, prompted the Kassigs to make a public plea for help.

"The dynamics have changed now. Steven's family kept to secrecy, and he was executed. Peter's name has been listed," Ed said.

Their only son Peter grew up in suburban Indiana loving fishing and hiking. After serving briefly in Iraq, Peter found his calling: delivering aid to Syrians brutalized by the civil war.

"He always was a compassionate person, and this was just something he felt he needed to do," Paula said.

It was on one of those missions when he was taken. Ed found out through a phone call the day it happened from a friend of Peter's in Syria.

"It was Peter's number. And I thought, 'Oh man, I get to hear from Peter.' And when I picked up the phone, I didn't recognize the voice," Ed said. "And the individual introduced himself. And-- we learned that he had been detained."

Once the video appeared, showing their son being threatened by ISIS, Ed and Paula retreated to a hotel to avoid the media.

Ed described his reaction one morning at breakfast when images of his son flashed across the TV.

"One minute you look at your scrambled eggs and you look up, it's football. Next minute, look at your scrambled eggs, you look up and there's your son," he said. "And you sit there and you have to watch. Everybody's jaw on the place drop. And you gotta fake it, too, 'cause you don't want to stand there and look callous. And inside, you just want to scream. 'Hey, that's my kid.' Just ate it, went back upstairs."

The Kassigs revealed, for the first time, that they received a horrifying audio recording of their son two weeks ago. He said his life was in jeopardy if U.S. airstrikes didn't stop.

It was the first time she had heard his voice in over a year.

Now the Kassigs are asking for mercy, appealing directly to ISIS through YouTube and Twitter messages.

Paula said she's not sure that the pleas are falling on any ears willing to listen.

"But I have to try. Because I need to know that I've done everything I can do," she said.

Ed said his son's captors have not asked for anything the couple can provide.

"They demand. They simply demand," he said.

"Their demands have always been ones that we cannot accommodate," Paula added.

It's beyond what's reasonable in terms of both money and power, she said.

"We have sent them back messages that we cannot do what you ask. We have tried. But we don't have the power to do it."