Algeria, Morocco and Tunisia are among 14 countries whose citizens the European Union believes to be “safe” enough from the coronavirus to allow in from 1 July, but the UAE, the United States and China are not included in a list unveiled on Tuesday.
Brazil, India and Russia are among the other major countries not to make the list because of their high number of Covid-19 cases.
Australia, Canada, Georgia, Japan, Montenegro, New Zealand, Rwanda, Serbia, South Korea, Thailand and Uruguay made the cut.
The EU said China is “subject to confirmation of reciprocity,” meaning it must lift all restrictions on European citizens entering China before it will allow Chinese citizens back in.
The "safe" countries would have to lift any bans they might have on European travellers and the list will be updated every 14 days.
Some southern countries in the EU such as Greece, Italy and Spain are desperate to welcome back tourists for the summer season to kick-start their ailing economies but splits reportedly remained over keeping a balance between economic growth and maintaining control of Covid-19.
More than 15 million Americans are estimated to travel to Europe each year but cases continue to rise in the world's worst-affected country, with more than 126,00 deaths from Covid-19 although the figure is almost certainly higher.
European countries have slowly begun to emerge from months of lockdown, although localised outbreaks have been reported in parts of Germany and the UK.
The EU imposed restrictions in March on non-essential travel to its 27 nations, plus Iceland, Liechtenstein, Norway and Switzerland, which are part of the Schengen open-borders area, to halt the spread of the virus.