Iceland previously announced that non-EU citizens will be eligible as well, however, rules are way too complicated and you risk being stuck at the airport if they run out of testing capacity for that day. Accepting recent negative tests performed outside Iceland is no longer an option, according to recent updates. Furthermore, Iceland may change their mind if uniform solution for internal borders is adopted (which may actually happen by mid-June). If they get an option to join the border-free regime with Europe provided they keep the external border closed (or stick to uniform rules), they will most likely opt to accept that deal, effectively closing themselves to US visitors.