"The reaction must be equally clear. Playing it soft is hardly an option," writes Bildt.
The tariffs will be 10 percent and will apply from February 1, according to Trump - who is threatening to then raise them to 25 percent on June 1 if the US is not allowed to take over Greenland.
In addition to Sweden, the threat also applies to Denmark, Norway, France, the United Kingdom, Germany, the Netherlands and Finland.
The US-European trade agreement that was concluded this summer is awaiting approval by the European Parliament.
Bildt writes that Trump's actions "will in all likelihood" cause the agreement to collapse.
“The confrontation is starting to heat up.”
