The campaign, which is being piloted in the Glasgow office of the UK Border Agency, was revealed by The Herald last week.
MSPs including Patrick Harvie (Green), John Mason (SNP), Joan McAlpine (SNP) and Jamie Hepburn (SNP)are among those who have backed the motion.
The motion was lodged after details of the campaign emerged. One poster on display shows an aircraft with the caption: "The plane can take you home. We can book the tickets."
Other slogans included: "Is life here hard? Going home is simple."
The motion states the parliament "strongly condemns" the actions of the Home Office in "trying to intimidate and harass asylum seekers".
It added: "[The parliament] deplores what it considers this attempt to instil fear and intimidate some of the most vulnerable people in society; urges the UK Border Agency to immediately cease what it considers this abhorrent pilot scheme, which is also taking place in Hounslow, London, and believes that Scotland should have a humane asylum system that recognises the inherent worth of all human beings, regardless of where they used to call home, and supports them in making a life here in Scotland."
The campaign has been defended by the Home Office as part of a policy to provide sensitive advice and assistance to help failed asylum-seekers return home with dignity. Critics say the office is also used by asylum-seekers still in the system.
James Dornan MSP (SNP) has already written to Home Secretary Theresa May with demands the campaign is pulled.
The campaign follows the "Go home or face arrest" vans debacle earlier this summer which resulted in the Home Office being persuaded to drop its campaign following cross-party criticism. The Advertising Standards Authority was called into investigate the posters after complaints.