Cassis said he hoped the US would allow Iran the payment of food and medicine through financial transactions, despite economic sanctions imposed on Iran, swissinfo.ch reported.
"We want to help ensure that the civilian population, which is suffering under the new sanctions regime, is supplied with basic necessities," Cassis is quoted in a Foreign Ministry statement.
He was speaking following official talks with the US Secretary of State, Mike Pompeo, on Sunday.
However, Cassis cautioned that Switzerland’s hands are tied if there is no willingness on either side to agree to talks.
Switzerland has been representing US interests in Iran for nearly 40 years and is hoping to take over a similar task with protecting power mandate in Venezuela.
Cassis also mentioned the importance of a multilateral cooperation within the United Nations.
On Saturday, Pompeo took part in a session of the closed-door Bilderberg conference on Lake Geneva and paid a private visit to the Swiss capital, Bern.
It was the first official visit by an US foreign minister to Switzerland in more than 20 years.