The two are the only Pacific countries on the list of 70 nations which Ukraine defines as being at migration risk.
The new vetting measures don't apply to heads of state and government, members of parliamentary and government delegations.
Cruise ship visitors are also exempt.
The new measures target Russian citizens who are now subject to a tighter registration process.
The list of 70 includes large African, Middle Eastern and Asian countries, such as Nigeria, Egypt and Pakistan as well as all former Portuguese colonies in Africa.