The EU has named 14 countries whose citizens are deemed "safe" to be let in from 1 July, despite the pandemic - but the US, Brazil and China are excluded.
Those named include Australia, Canada, Japan, Morocco and South Korea.
The EU is ready to add China if the Chinese government offers a reciprocal deal for EU travellers, diplomats say.
Many border controls have been lifted for EU citizens travelling inside the bloc. Rules for UK travellers are part of the current Brexit negotiations.
But UK nationals are still to be treated in the same way as EU citizens until the end of the Brexit transition period on 31 December, the EU Commission says.
So during this period UK nationals and their family members are exempt from the EU's temporary travel restriction.
On the current "safe" list, still likely to be amended, are Algeria, Australia, Canada, Georgia, Japan, Montenegro, Morocco, New Zealand, Rwanda, Serbia, South Korea, Thailand, Tunisia and Uruguay.
EU nations in the 26-member Schengen zone normally allow passport-free border crossings for EU citizens, but national authorities have reimposed restrictions in this crisis.
The UK is currently negotiating temporary "air bridges" with several EU member states, so that coronavirus does not totally block summer holidays - the busiest season in Europe for tourism, which employs millions of people.
BDST: 1847 HRS, JUN 30, 2020