The case is now being treated as a murder inquiry.
The Press Association reported that, writing in the Find Gaia Facebook group, Natasha Pope said: “I believe in this community and I believe miracles can happen.
“I am holding on to hope, along with Gaia’s sisters and the whole people who are my strength. Please hold on with us.”
Police have stated clothing discovered on Thursday on open land north of Swanage appeared to be Pope’s and matched what she was dressed in when she was last seen.
She was last seen dressed in a red checked shirt with white buttons, grey and white woven leggings and white trainers.
The discovery was made by a member of the public in an area of open land north of the coastal path.
The 19-year-old, who has epilepsy and did not leave with her medication, vanished on the afternoon of 7 November.
On Friday night, volunteers were out with torches scouring acres of the Dorset countryside in an attempt to find the 19-year-old.
So far, three people have been arrested on suspicion of murder.
A 71-year-old woman and a 19-year-old man were released under investigation on suspicion of murder on Tuesday following their arrest the previous day.
Volunteers are being asked to join mass searches of Swanage today. People are being asked to gather at midday at three separate locations to join line-searches.
Anyone with advice is asked to contact Dorset Police at www.dorset.police.uk, via email email@example.com or by calling 101, quoting event number 14:108. Alternatively contact Crimestoppers anonymously on 0800 555 111 or via www.crimestoppers-uk.org.