UK
13 October 2014
Last updated at 17:00 ET
In a statement, his sister Jessica said it was "simply not accurate" that there had been no attempts to engage with IS.
She also "strongly" challenged the group to reopen a previous channel of communication and restart dialogue.
Jessica Cantlie said she was speaking on behalf of her terminally-ill father, Paul, who recently spoke of his "despair and helplessness" at his son's plight in a separate appeal to IS.
'Frustrating'
"We had previously been in contact through a channel started by you. But this stopped for reasons best known to you."
The videos of Mr Cantlie, who is originally from Hampshire, have all followed the same format, with the journalist sitting at a desk against a black backdrop to address the camera.
There are no signs of violence in the videos but, in the first, Mr Cantlie made it clear he was speaking as a prisoner whose life was in danger.
Referring to the most recent video of Mr Cantlie released by IS, and an online article alleged by the militants to have been written by him, she said his words "are powerful and have huge resonance".
John Cantlie has been held hostage since he was kidnapped in Syria in late 2012
Mr Cantlie had also previously been kidnapped in July 2012
IS, also known as Isis or Isil, has taken control of large areas of Syria and Iraq and declared a caliphate.
Since August, the group has killed four Western hostages - US journalists James Foley and Steven Sotloff and British aid workers David Haines and Alan Henning.
Referring to the British victims, Ms Cantlie said: "Sadly like the families of David Haines and Alan Henning, before they were killed, our efforts at re-opening dialogue continue to be ignored by those holding John.
"We strongly challenge those holding John to return to your previously-opened channel, to which we continue to send messages and await your response so that in keeping with everyone's wishes, we can restart dialogue.
"We implore IS to reinitiate direct contact."
Mr Cantlie - an experienced journalist and photographer - has twice been held captive in Syria.
He was kidnapped in July 2012, and handcuffed and blindfolded for a week, but escaped with the help from the Free Syrian Army.
The second kidnap happened when he returned to Syria towards the end of 2012.
by Emily Straton and Biodun Iginla, BBC News, London
The sister of British hostage John Cantlie has appealed for "direct contact" with the Islamic State (IS) militants holding him.
The journalist, who was kidnapped in Syria in 2012, has appeared in several videos released by IS. In a statement, his sister Jessica said it was "simply not accurate" that there had been no attempts to engage with IS.
She also "strongly" challenged the group to reopen a previous channel of communication and restart dialogue.
Jessica Cantlie said she was speaking on behalf of her terminally-ill father, Paul, who recently spoke of his "despair and helplessness" at his son's plight in a separate appeal to IS.
'Frustrating'
Continue reading the main story
“Start Quote
Jessica CantlieWe implore IS to reinitiate direct contact”
Ms Cantlie said: "It is not true to say there has been no attempt to engage with IS. This is simply not accurate.
"This is frustrating for all parties, including those who are trying to assist us."We had previously been in contact through a channel started by you. But this stopped for reasons best known to you."
The videos of Mr Cantlie, who is originally from Hampshire, have all followed the same format, with the journalist sitting at a desk against a black backdrop to address the camera.
There are no signs of violence in the videos but, in the first, Mr Cantlie made it clear he was speaking as a prisoner whose life was in danger.
Referring to the most recent video of Mr Cantlie released by IS, and an online article alleged by the militants to have been written by him, she said his words "are powerful and have huge resonance".
John Cantlie has been held hostage since he was kidnapped in Syria in late 2012
Mr Cantlie had also previously been kidnapped in July 2012
Since August, the group has killed four Western hostages - US journalists James Foley and Steven Sotloff and British aid workers David Haines and Alan Henning.
Referring to the British victims, Ms Cantlie said: "Sadly like the families of David Haines and Alan Henning, before they were killed, our efforts at re-opening dialogue continue to be ignored by those holding John.
"We strongly challenge those holding John to return to your previously-opened channel, to which we continue to send messages and await your response so that in keeping with everyone's wishes, we can restart dialogue.
"We implore IS to reinitiate direct contact."
Mr Cantlie - an experienced journalist and photographer - has twice been held captive in Syria.
He was kidnapped in July 2012, and handcuffed and blindfolded for a week, but escaped with the help from the Free Syrian Army.
The second kidnap happened when he returned to Syria towards the end of 2012.
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