The appeal came after a video, released by the IS militants, warned that Kassig would be killed next. The militants have killed four western hostages in recent weeks.
In their video message, Ed and Paula Kassig spoke about their son's vocation to help Syrian refugees and refer to him as Abdul Rahman, the name he adopted when he converted to Islam during captivity in Syria.
"At an early age our son was inspired by his grandfather to do humanitarian work. When he saw the suffering of the Syrian people, he went to Turkey and founded an organisation to provide aid and assistance," Ed said, who throughout the video mentioned his 26-year-old son's vocation.
"We implore his captors to show mercy and use their power to let our son go," they said in the video posted on YouTube with Arabic subtitles.
His mother Paula, wearing a scarf on her head to show respect for Islamic customs, spoke directly to her son in hope that he will be able to see the video.
"We are so very proud of you and the work you have done to bring humanitarian aid to the Syrian people," she says while holding his photo.
Kassig, the first soldier who served in the Middle East and later returned to the area on a humanitarian mission, has been missing for a year in Syria.