Newspaper Svenska Dagbladet reports that Sweden's defence minister Peter Hultqvist on Tuesday received a classified letter from Mattis that apparently outlines a tougher US position.
Sweden was among 122 countries that in July voted in favour of the UN Treaty on the Prohibition of Nuclear Weapons. Sweden's foreign minister Margot Wallström has indicated that Sweden intends to sign the treaty, along with other UN member states, on September 20th.
"The government's position on these weapons has been well-known for a long time," Wallström has previously told Svenska Dagbladet. She said that the government's analysis suggested that "bilateral and multilateral defence cooperation will not be affected" by Sweden signing the treaty.
The five countries classified as nuclear weapons states under the Non-Proliferation Treaty or NPT, have all boycotted the UN treaty, including the US.
Sweden also signed a Statement of Intent over joint defence cooperation with the US in June 2016.
Wilhelm Agrell, a politics professor at Lund university, told news agency TT that he does not believe Sweden signing the new treaty would have any immediate consequences.
"But it will definitively lead to even more concrete expressions of irritation from the American side," said Agrell. "This will perhaps be seen in bilateral contacts - visits at the highest level and such like," he added.
Radio Sweden has tried to reach Peter Hultqvist for a comment.