In a statement issued by the Foreign Office in London today, they said the extremists have not responded to any of their attempts to make contact so far.
"We are the family of David Haines. We have sent messages to you to which we have not received a reply. We are asking those holding David to make contact with us," the family said.
Scottish-born Haines, 44, was taken hostage in Syria in March 2013 and was threatened in a video released this month depicting the beheading by IS militants of the US journalist Steven Sotloff.
In a statement last week, ACTED said it was "deeply shocked" at the threats made against him.
"ACTED strongly condemns the violence and threats against David. A man's life should never be threatened on account of his humanitarian commitment," it said.