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The United States, Brazil and China are excluded, the BBC is reporting.
Along with New Zealand on the current Covid-19 'safe list' are Algeria, Australia, Canada, Georgia, Japan, Montenegro, Morocco, Rwanda, Serbia, South Korea, Thailand, Tunisia and Uruguay.
The EU is ready to add China if the Chinese government offers a reciprocal travel deal for EU citizens.
EU border controls have been lifted for EU citizens travelling inside the bloc.
Rules for UK travellers are covered separately in the Brexit negotiations.
UK nationals are still to be treated in the same way as EU citizens until the end of the Brexit transition period on December 31, so during that time they will be exempt from the temporary travel restriction.