The parents of the American aid worker who has been threatened with beheading in Syria released more of their son’s letter from captivity on Monday, as part of their campaign to get their son released.

Abdul-Rahman Kassig, formerly known as Peter, was captured on 1 October 2013 and is being held by Islamic State (Isis) militants. His family had asked for a media blackout after his disappearance, at the orders of Kassig’s captors.

The blackout remained in place until Kassig appeared in a video released last week, which showed the beheading of British aid worker Alan Henning. In the video, an Isis militant threatens to kill Kassig, which prompted his family to go public.

“We couldn’t answer honestly when people would ask us. So we had to lie to our friends again and again and again,” Abdul-Rahman’s mother Paula told CBS News in the Kassigs’ first television interview.

The Kassigs pointed to the killing of US journalist Steven Sotloff by Isis as a turning point. At one point, the two hostages had been cellmates.

“The dynamics have changed now. Steven’s family kept to secrecy, and he was executed. Peter’s name has been listed,” Ed Kassig told CBS News.

Kassig’s parents have asked people to refer to their son by the name he adopted upon converting to Islam in captivity, and not by his birth name Peter.

Ed and Paula Kassig during a prayer vigil for their son, Abdul-Rahman Kassig, in Indiana last week. Photograph: Steve C Mitchell/EPA

His mother Paula Kassig told CBS that the family has been campaigning for his release in the media and in direct messages to Isis through YouTube and Twitter. Kassig said they respond with demands that the couple cannot accommodate. “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,” Kassig said.

The family on Monday also shared more from a letter written by Abdul-Rahman that was carried out by a hostage who was released earlier this year. Kassig said in the letter:

“It is still really hard to believe all of this is really happening … as I am sure you know by now, things have been getting pretty intense. We have been held together, us foreigners … and now about half the people have gone home. … I hope that this all has a happy ending but it may very well be coming down to the wire here, and if in fact that is the case then I figured it was time to say a few things that need saying before I have to go.”

He then thanked his parents, as seen in a part of the letter that was previously released and goes into details about his physical and mental state. “Physically I am pretty underweight but I’m not starved, & I have no physical injuries, I’m a tough kid and still young so that helps,” Kassig said. “Mentally I am pretty sure this is the hardest thing a man can go through, the stress and fear are incredible but I am coping as best I can. I am not alone.”

He said the captors told hostages that their families no longer cared about them.

“They tell us you have abandoned us and/or don’t care but of course we know you are doing everything you can and more. Don’t worry Dad, if I do go down, I won’t go thinking anything but what I know to be true. That you and mom love me more than the moon & the stars.”

The family said on Monday that it had received an audio recording of their son just before his identity was made public. In the recording, the details of which have not been released, Kassig says his time is running out.

The Kassigs explained why they are undertaking this media campaign in an interview with NBC News, which is set for broadcast on Monday night.

“I am hoping that he will somehow hear of this and of other conversations we’ve had or other times we’ve spoken in public,” Paula Kassig said. “That way he’ll know that we haven’t forgotten him, we haven’t abandoned him and we certainly do love him.”