Löfven made the announcement in an interview Thursday with newspaper Dagens Nyheter.
The apprentice positions would have been government subsidized additional jobs within health care and social services, and were supposed to be given to unemployed youths. The dual aim was to help them enter the workforce and to address the shortage of workers in those sectors.
Both the Alliance parties and the xenophobic Sweden Democrats oppose this proposal.
The prime minister also says the Social Democrats would cooperate with a potential conservative government if his green-red coalition loses power in next March's extra election.