Cathie Joyce told Premier that since 72-year-old John Joyce disappeared, "his family and friends are very, very worried and shocked".
Mr Joyce went missing over six weeks ago, three days into a six day pilgrimage to Fatima.
On 14th July at 9:20 am he walked with his pilgrimage group to a studio nearby to see a video about the Children of Fatima. It finished at 10:45 am and one of the group saw him in front of the Basilica about 10 minutes later, where he was last captured on CCTV in the Portuguese town.
Mr Joyce, from Sheffield, South Yorkshire has not been seen or heard from since then.
Cathie Joyce told Premier that he had "left his passport, money, mobile, reading glasses, hat...in his hotel, so was obviously not intending to go far before returning to the hotel for lunch at 1pm."
The family fears this indicates something sinister may have happened to him.
Cathie Joyce told Premier: "If he had collapsed, fallen or been taken ill in town he would have been seen and cared for. Fatima was full of pilgrims and visitors that day.
"If he had strolled out of town and been taken ill or fallen he would have been found by now. The family has now been forced to contemplate 'darker' scenarios. Was John either beguiled into accepting a car ride or taken by force to somewhere else? Is he now being held against his will by a group or cult or for some other purpose eg. organ removal?"
The Joyce family are appealing to anyone going to Fatima to be on the lookout for John who they say may now have a beard and "may be very unkept looking and dirty".
Mr Joyce is missing his lower denture and speaks a little Portuguese but with an English accent.
The family is also appealing to anyone who was in Fatima on 14th July 2017 and was taking photos, to check to see whether they accidently captured Mr Joyce's image, wearing a blue checked shirt and blue shorts as seen in the CCTV image.
They expressed their "deep gratitude to the local parish priests and congregations close to where John lives in south London, who have held several Masses for John, and to the many friends and family in the UK, Ireland, USA and Australia who have offered prayers and Masses for John and for us, his family".
The British Embassy in Portugal is understood to be helping in the hunt for Mr Joyce as well.
Anyone with information can contact the Lucie Blackman Trust on 0800 098 8485, email any information to [email protected], or contact the local Fátima GNR police on (+351) 249 530 580.