Claudia Lawrence, who was 35 when she disappeared, was last seen in York on March 18, 2009 and police believe she has been murdered, although no body has ever been discovered.
University of Hull student Miss Squire was reported missing on February 1 following a night out with friends in the city.
Miss Lawrence’s father Peter, 72, from York, said he empathised with the 21-year-old’s family, who have made a number of appeals and released information about their daughter since her disappearance.
Speaking to The Press Association, Mr Lawrence said: “You just feel for her family.”
Asked if he had a message for the student’s parents, Lisa and Russ Squire, he said: “Keep up hope at this stage.
“It’s only a month, that’s bad enough, but you’ve got to keep hope.”
Mrs Squire said in a previous statement that it had been “a month of utter heartbreak and despair”.
The parents, from High Wycombe, Buckinghamshire, said the time since Miss Squire went missing had been one of “unending torture”, but they still hope she will be found.
They described their daughter as a “very thoughtful and caring young woman who puts others before herself” and said she is “much loved” by her three younger siblings.
Humberside Police have said that despite following up hundreds of leads and carrying out intensive searches, Miss Squire’s disappearance remains unexplained and they fear “she has come to harm”.
Pawel Relowicz, 24, from Raglan Street, Hull, was arrested on suspicion of abduction in connection with Miss Squire’s disappearance and remains under investigation.
He has been charged with 12 unrelated offences and has been remanded in custody.
A total of nine people have been arrested or interviewed under caution in connection with Miss Lawrence’s disappearance but no-one has been charged.