Germany has taken cautious steps to ease its coronavirus lockdown, allowing small shops to reopen last week.
But in a blow to its tourism sector, its warning against worldwide travel has now been extended until 14 June.
Foreign Minister Heiko Maas said Germany's fight against the pandemic was not at a stage where he could "recommend carefree travel".
"People won't be able to spend a holiday as they usually know it, on full beaches or in full mountain huts."
Germany warned on Wednesday that its economy could shrink by a record 6.3% this year.
"We will experience the worst recession in the history of the federal republic" founded in 1949, Economy Minister Peter Altmaier said.
In common with several other EU states, Germany closed some of its land borders last month to try to curb the spread of Covid-19, and repatriated 240,000 German travellers from abroad.
The German association for tour operators said it had lost over €4.8bn ($5.21bn) in sales up until the end of April, and said the tourist sector would now need urgent government assistance.
What are other European countries doing?
Tourism accounts for 10% of the EU's economic output, and the 27 member states must now decide how to resume public movement both within their countries and beyond.
Croatian Tourism Minister Gari Cappelli has called for "tourist corridors" to be created between EU countries, with epidemiologists deciding the rules for movement. There have been reports that Czech tourists could be allowed into Croatia in July and August.
Austria, which has lifted quarantine restrictions at three popular ski resorts, may adopt a phased return to tourist activity that begins by allowing German visitors in.
In Spain, hotels are allowed to reopen from 11 May with social distancing in force - but the proposal has angered the Hotel Business Association of Madrid. The body expressed its "serious concern" over the plan on Wednesday, and shared its "disbelief" that the government wanted to reopen hotels "when the arrival of clients is impossible" due to border closures and lack of flights.
France's exit from lockdown is expected to commence in earnest on 11 May, but Prime Minister Edouard Philippe said travel won't become unrestricted there. Journeys of more than 100km (62 miles) will be allowed "solely for compelling family or professional reasons".
Calls for airline voucher system
Airlines have been severely hit by the grounding of planes, and 12 EU states want travel rules to be changed so that airlines can compensate passengers with vouchers rather than cash for cancelled flights.
Neighbouring countries are also trying to handle cross-border workers. Germany has relaxed a quarantine on Polish commuters but Poland has not yet followed suit. Hundreds of people staged protests in Polish border towns last week.
While Poland said it would reopen hotels and shopping centres from 4 May, there was no indication of when borders would reopen.
Is anyone opening up beaches?
If and when beaches are reopened, they may only be accessible to those living locally.
In Belgium, mayors from towns along the North Sea coast have agreed to reach a decision by 8 May on how to restrict beach access and "save the Belgians' summer".
France has said no beaches will be open until at least June, while Spain is also targeting the end of June.
Travel from one part of Spain to another will also be restricted until June.
Authorities in the Spanish coastal resort of Zahara de los Atunes recently caused an outcry by spraying a beach with bleach in an attempt to protect children from the coronavirus.