After the meeting, Keller-Sutter spoke only of “a very friendly and open exchange on common issues”.
The Swiss Government said that it would hold an extraordinary meeting.
Swiss businesses worry that competitors in other wealthy economies will have an edge, with the European Union and Japan having negotiated a 15% tariff and Britain securing a rate of 10%.
“The horror scenario materialises,” Swissmem, the association of the mechanical and electrical engineering industry, said in a statement.
“If this horrendous tariff burden remains in place, it will mean the de facto death of the export business of the Swiss tech industry to the USA - in particular given the much lower tariffs for competitors in the EU and Japan.”
The group urged the Government to continue to negotiate with the US, “even if the chances of success currently appear to be slim”.
The tariff jeopardises entire sectors of the export-heavy Swiss economy, notably watchmaking and industrial machinery, but also chocolate and cheese. Tens of thousands of jobs could be threatened.
Trump justified his action by the fact that Switzerland has a trade surplus of tens of billions of dollars with the US.
Nearly 19% of Swiss goods exports went to the US last year, according to customs data.
Switzerland’s pharmaceutical industry, a major exporter, has been exempt so far but Trump has announced plans to hit the global sector with a separate tariff.
Switzerland had argued that the US enjoys a significant services trade surplus, which balances the relationship, and that Swiss firms are among the top investors in the country.
It also noted that most American industrial goods enter Switzerland tariff-free.
-Agence France-Presse