Brussels is calling on EU countries to open borders to travellers from outside the bloc from July 1.
European countries have gradually begun to lift internal border restrictions, put in place to stop the spread of COVID-19.
Now the European Commission is urging members of the Schengen visa-free travel area to coordinate on how external borders are opened.
"International travel is key to tourism and business, and for family and friends reconnecting," EU Commissioner for Home Affairs, Ylva Johansson, said.
The lifting of the travel ban is dependent on EU countries opening up their internal borders around June 15.
"You should open up as soon as possible," said Johansson when asked about internal borders, explaining that the European Centre for Disease Control had said internal borders was "not an effective way of dealing with the pandemic now".
But not all countries plan to reopen borders to EU travellers next week, with Spain and Portugal set to reopen later in June and with Denmark only planning to open borders with Germany, Iceland and Norway.
The European Commission is now asking member states to agree on a list of non-EU countries where travellers could come from starting from July.
Conditions for lifting restrictions to non-EU countries will include looking at the infection rates and the country's capability to deal with the virus. Restrictions should remain in place for countries with a worse outbreak.
"It will apply to all countries in a similar or better [outbreak] situation to the EU," Johansson said, clarifying that not all external borders should open from July 1.
Exceptions to restrictions will apply to students, as well as highly-skilled non-EU workers.
The EU has recommended that travel restrictions are lifted for Albania, Bosnia and Herzegovina, Kosovo, Montenegro, North Macedonia and Serbia.