In a Tweet, Berset lauded the “excellent friendship” between the two countries and said they were ready to strengthen it further.
He described Switzerland and the US as “among the most innovative countries in the world”.
President Trump also tweeted that the meeting had been "great" and spoke of the "honour" of being in Switzerland.
Speaking at a news conference following the bilateral meeting, Berset said the two countries wanted to work more closely together to solve global problems, the Swiss news agency SDA reported.
SDA quoted Trump as saying that he would be returning to the US with a lot of goodwill from Switzerland.
Trump said that as a big investor in the US Switzerland had greatly benefited from the massive jump in the stock market.
“I have made Switzerland even richer,” Trump said, according to SDA.