In a statement following British PM Theresa May's triggering of Article 50 to formally initiate the process of the UK leaving the EU, Löfven said that Sweden wanted the negotiations to find a "good solution for EU citizens exercising their right to settle in the UK, and vice versa".
He also called for a financial solution where the UK "pays for the commitments it has made".
"In future relations between the EU and the UK we want trade relations to be as favourable as possible and effective cooperation in other areas, including security," Löfven's statement reads.
"The UK has been a close and valuable partner in the EU. We regret Britain's decision to leave the union, but it is good that the negotiation process can now begin after quite a long waiting period. I welcome the constructive approach in Prime Minister May's letter. I want to see orderly and results-oriented negotiations, and that, even after the withdrawal, we have as positive and mutually beneficial a relationship with the UK as possible. That's important for the UK, for the EU, and for Sweden," Löfven also noted.
In February, Sweden's EU affairs and trade minister Ann Linde told The Local that it is important that people who "used their rights as EU citizens don't become a bargaining chip in the Brexit negotiations".