Svenska Dagbladet (SvD) reports that the letter was registered at the Swedish Department of Defence on Tuesday, and regards Sweden's intention to sign a treaty banning nuclear bombs when it opens for signatures from any UN member state in September.
The treaty was first backed by 122 countries including Sweden in a vote at the New York UN headquarters in July, but countries with nuclear arms boycotted the conference, as did some of their allies.
According to SvD, Mattis warned in the letter that Swedish-American defence cooperation would be hampered if Sweden signs the treaty.
"The implication is that if the government signs the convention banning nuclear weapons, including on Swedish territory, it would impact both defence cooperation during peace time and the possibility of military support from the USA in a crisis situation," SvD claims.
Earlier in August, Sweden’s Foreign Minister Margot Wallström wrote that the government intended on signing the treaty, and "Sweden’s vote in favour was entirely in line with our disarmament policy as part of a broader security policy".
"Our initial assessment shows that our bilateral and multilateral defence cooperation, including our partnership with Nato and cooperation with the United States, France and the United Kingdom, can continue," she added.