Members of the Kronoberg county council voted on the proposal earlier this week. The decision to investigate the matter further was voted through by a majority including members of the local Moderate, Centre and Christian Democrat parties.
But the development is troubling Sweden's Social Democrat Prime Minister.
"I'm concerned that they are starting to discuss in this direction. Should we pursue this line, we will soon have others who will refuse to treat something else. This is not good. We should have national guidelines and this means you should be treated in the same manner, regardless of which county you live in," Löfven told the TT news agency.
However the move has been welcomed by Swedish nurse Ellinor Grimmark, who was fired last January for refusing to perform abortions due to her religious beliefs.
Grimmark had a contract offer rescinded at a Swedish hospital after she said she wouldn't perform abortions.
She enlisted the help of an American Christian legal organization and took her case to court after Sweden's Equality Ombudsman (Diskrimineringsombudsmannen or DO) said she hadn't been discriminated against.
"Freedom of conscience is very clearly defined. It involves issues of life and death. It's about abortion and euthanasia," Grimmark told Swedish newspaper Aftonbladet.
The Swedish nurse has since moved to Norway, where abortion refusal is permitted among healthcare professionals.
She added: "I want to be there when a little life comes into the world and takes its first breath. But I am in no way capable of performing abortions."
Meanwhile local media reported that members of the Moderate and Liberal were saying no to the proposal.
"There should be no doubt where we stand as moderates when it comes to abortion legislation," Suzanne Frank, county commissioner for the Moderates told the Smålandsposten newspaper.
She added that any proposal to investigate the so-called freedom of conscience clause should be conducted on a national level.
The proposal came first from the members of the local Christian Democrat party and received support from both Moderates and the Centre Party, while the Liberal Party abstained from voting.
In the past the Swedish Association of Health Professionals (Vårdförbundet) has said that patients should know what to expect when they enter a Swedish hospital.
"As a patient in Sweden it must be very clear what (healthcare) you can expect according to Swedish law. It should not depend on whom you happen to encounter," Vice chairwoman Pia Arndorff told TT.