Two petitions have been handed to the federal government demanding more sanctions are placed on Iran.
The organisation, Free Iran Switzerland, says members of the Iranian government should be banned from Switzerland, Iranian funds frozen and the Iranian Revolutionary Guard should be classed as a terrorist organisation.
Campaigners say there should also be no deportations to the country.
Switzerland has implemented some measures brought in by the UN and the EU.
One parliamentarian, Fabian Molina, says when human rights are trampled on, then Switzerland must take a stand.
G7 Summit in Évian - Everything you need to know
Geneva braces for G7 with 4,000 soldiers as protest standoff deepens
Zelensky proposes Switzerland as venue for Putin meeting
Geneva family fights to recover dead son's brain
Airport queues lengthen at Geneva and Zurich under new EU border checks
Ticino votes on Switzerland's first compulsory dental insurance
