The figures showed 3511 students had enrolled with SJS in the year to the end of October, a 42% increase on the same period last year, when 2474 enrolled.
The numbers of students placed in work through SJS was down 13% on last year.
Mr Edgar said the figures painted a "grim picture of how tough students are doing it financially".
"The latest unemployment figures show it's tough out there for everyone, but it's important the public see the opportunity SJS offers for one-off and part-time employment needs," he said.
The figures came at a time when many students were looking for holiday jobs.
"Students are now going into summer holidays, so there's a real opportunity for the public and private sectors to make the most of the students' break and, at the same time, give them extra experience to add to their CVs."
Psychology student Matt Cox, who has just completed his degree, said he was struggling to find work for summer and was considering applying for the unemployment benefit.
He said it was never easy to find holiday work in Dunedin because of the "sheer number" of students looking for jobs, but the job market seemed to be "a bit tougher" this year.
OUSA student support centre manager Matt Tucker said in the year to the end of October, it had provided 465 food packages to students, which was about the same number as last year.
The difficult job market meant some University of Otago students who expected to be able to find work were unable to, Mr Tucker said.
This meant they were reliant on the student allowance or their student loans to get by, which students were saying did not allow as much "discretionary spending" as in the past, he said.