The call comes after a string of recent reports in the Swedish media about people with stable jobs being forced to leave Sweden due to the new law, which came into force in April.
"I think that people who have made an effort and have done everything we asked of them also deserve to be able to stay," Douglas Thor, the chair of Moderata ungdomsförbundet (MUF), told the Swedish public service radio broadcaster SR.
Sweden's parliament voted in the spring to abolish the so-called spårbyte or "track change" law which allowed rejected asylum seekers to apply for a work permit without having to leave Sweden.
But in recent weeks there have been a series of media reports of immigrants being forced to leave Sweden as a result of the law, despite being both employed and well-integrated, with the case of Sara Ghorbani Shamasbi, her husband Farhood Masoudi, and their son Parhan in Norsjö, Västerbotten, reported by the Aftonbladet newspaper.
Shamasbi has a permanent job with a cleaning company and Masoudi works in elderly care, both sectors where the municipality is desperate for workers.
Håkan Jansson, who represents the Moderate Party on the Norsjö municipal council, has also called for the law to be changed.
"These people have done exactly what we asked of them, especially us Moderates. We should stand by what we have said," he said. "I am a Moderate, and we Moderates pushed the button – we abolished the track change law – and I have to take responsibility for that. However, I have been critical of how it was handled afterwards. I don't think this was well thought out."
The Swedish Migration Agency estimates that a further 2,600 people risk being deported because of the law being abolished.
Migration Minister Johan Forssell, however, said he was against revisiting the decision to abolish the law, and said that those forced to leave Sweden could instead apply for a new work permit from their home country if they can meet the new raised salary thresholds.
"That possibility obviously applies to those people who have a decision like this due to spårbyte. That possibility exists and you can then come back if you meet the salary requirements that apply."
Thor rejected this argument, saying that this would require those concerned to abandon all the progress they have made and start their careers in Sweden again from scratch.
"It's a bit like someone getting a building permit and who has already started building and who is then made to demolish everything they've built and then build it back up just to make the bureaucracy work properly."
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