Speaking in the White House East Room following their meeting, Trump said that it was thanks to Swedish negotiations that American student Otto Warmbier was released from North Korea last year, where he was being held in prison while in a coma. Warmbier later died after returning to the US.
Löfven offered the President further help with US-North Korea relations.
"Sweden can be a channel. Because we have a long presence in the Korean peninsula and trust from both the north and the south, we can have some input. I've conveyed that to the President," the PM said.
Unlike many countries Sweden has a diplomatic relationship with the North Korean dictatorship and an embassy in Pyongyang. It also acts as a protecting power for the US in the country.
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The subject of Trump's controversial plans to impose tariffs on imported steel and aluminium was also on the agenda. Löfven insisted that free trade is important for the EU, but Trump appeared unwavering in his decision and said the EU had been unfair and tough towards the US.
"Trade wars aren't so bad," Trump insisted, adding that the tariffs will be done "in a loving, loving way".
Löfven later told Swedish journalists outside the White House that a trade war was not the way forward.
"According to my understanding the excess steel is mostly Chinese, because they account for 50 percent of global production, and the EU for less than 10 percent. I think it's better for the EU and USA to find some way to cooperate in order to deal with the situation."
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The PM added that such a negotiation would have to be carried out at EU level and any possible exemption for countries or companies was not discussed with Trump.
The PM and President have very different political views, but the Swedish leader did try to point out one similarity at the end of the press conference, saying they are both "political outsiders" while recalling his background as a welder.
IN PICTURES: Swedish PM Löfven meets US President Trump
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