Just 70 per cent of 18 to 29-year-olds have received a vaccine, despite jags being available to all adults.
Coverage in age groups over 55 is 100 per cent.
The National Union of Students said it was “particularly concerned” about the risk of Covid spread among unvaccinated young people entering student accommodation when the autumn term starts.
"The Scottish Government must urgently consider what more can be done to protect students and wider society from the spread of Covid-19,” said union president Matt Crilly.
The Scottish Greens have also called for more to be done, especially around college and university campuses.
Party health spokesperson Gillian Mackay said: “Drop-in centres sometimes aren’t an option for young people who are self-isolating or who can’t get to the location easily.”
Ms Mackay urged the Scottish Government to “reach out to young people using the services they are already accessing like colleges and universities”.
She said messaging must be clear that young people are not immune to risk from Covid, calling the recent UK Government lifting of restrictions and associated messaging “unhelpful” on this point.
“Just because Boris Johnson thinks it is acceptable to experiment with letting young people catch the virus doesn’t mean we need to accept it in Scotland,” she said.
Behavioural scientist Linda Bauld said key methods to increase uptake are good communication, ease of access and possibly incentives.
While vaccine passports are “controversial”, Professor Bauld pointed to countries like France and Italy where these have been used as incentives to increase vaccine uptake.
"It may have a role to play, but I think it’s quite a big jump to say we should do it for lots of settings,” she said.
"What I would prefer is that we just try and keep up the comms to young people. Targeted, regular communication, using social media and other platforms that are easily accessible to them.
"Relatively few young adults are watching briefings from the First Minister. They are valuable, but that's probably not the target audience.”
Prof Bauld said vaccine centres should be targeted in places where young people work and interact.
There is not much evidence for celebrity endorsements encouraging uptake, she said, but quirky ideas like the endorsement of vaccines by dating apps, which allow people to put vaccination stickers on their profiles, are “great”.
“We have to change social norms so that it’s viewed as something that is attractive and acceptable,” she said.
A Scottish Government spokesperson said: “Universities and colleges are already encouraging students to get vaccinated as soon as possible so they will be fully vaccinated before arriving on campus.
"We have also agreed with health boards, and higher and further education institutions to appoint single points of contacts in universities and colleges who will support the delivery of the vaccination to students across Scotland, including through the use of on-campus vaccination clinics.
“We want to thank everyone who has taken up the offer of a vaccine and, of course, all those who have worked on the programme since day one. Drop-in clinics continue to operate or you can arrange an appointment at a time and location to suit at NHS Inform.”