The European Commission has recommended travel to the EU from selected non-EU countries be allowed to restart from July 1.
However, Germany extended its foreign office advice against all but essential travel to most of the world until the end of August this week.
The EC announced on June 11 that restrictions on non-essential travel to the EU should end on June 30, as many Schengen area states prepare to lift internal border restrictions next week.
Europe’s Commissioner for Home Affairs, Ylva Johansson, said: “We are proposing a clear and flexible approach towards removing restrictions on travel to the EU starting on 1 July.
“While we all have to remain careful, the time has come to make concrete preparations for lifting restrictions with countries whose health situation is similar to the EU’s.
“It will apply to all countries in a similar or better [outbreak] situation to the EU.”
Johansson told member states: “You should open up as soon as possible.”
However, German government advice against travel to 160 countries was extended to August 31 and includes travel to Turkey.
Berlin said it would lift the advice for countries where the spread of the virus has been curbed, taking account of the number of new Covid-19 cases, testing capacity, hygiene rules and health system capacity.
The extension came as Germany prepares to lift border controls on intra-EU travel from June 15, although some restrictions on EU travel will remain longer
Flights from Spain will only be allowed to land in Germany from June 21.
The EC proposes member states agree a list of non-EU countries from which travel can resume.
The Commission said: “The restriction should be lifted for countries selected by member states, based on the health situation, the ability to apply containment measures during travel, and reciprocity considerations.”
Data from the European Centre for Disease Prevention and Control (ECDC) and World Health Organisation (WGO) will also be taken into account, and restrictions reintroduced if a country is judged no longer to meet the criteria.
The EC noted: “Member states can still refuse entry to a non-EU traveller presenting a threat to public health, even coming from a country for which restrictions were lifted.”
It recommended travel restrictions for Albania, Bosnia and Herzegovina, Kosovo, Montenegro, North Macedonia and Serbia also be lifted from July 1 because “their epidemiological situation is similar or better than that of the EU”.
International students and highly-skilled non-EU workers will be exempt from restrictions on non-EU entry.
Greece has said it will welcome travellers from non-EU countries including Australia, China and South Korea from June 15.