Most of them are thought to have been trekking in the Everest or remote Langtang regions. Many are hoped to be alive but isolated by the quake.
The fate of thousands of Nepalese in remote communities is also unknown.
Nepal has called for more foreign help and humanitarian aid, admitting it was ill-prepared for the disaster.
The Nepalese authorities say the death toll from April 25 quake could rise to 10,000.
Nearly 14,000 people were injured in the disaster. Relief and rescue teams have reached most areas but many people remain in urgent need of humanitarian assistance.
The 7.8-magnitude earthquake struck during peak trekking season in a country popular with mountaineers. Twelve EU citizens are known to have died so far. Some of them were killed by avalanches, triggered by the quake, that struck base camp below Mount Everest.
The EU envoy to Nepal, Rensje Teerink, said the authorities did not know the whereabouts of some 1,000 other EU citizens.
“They are missing but we don’t know what their status is,” she told reporters in the capital, Kathmandu.
Another EU official, speaking to the AFP news agency on condition of anonymity, said most of the missing were likely to be found safe.
Many backpackers do not register with their embassies in Nepal, which has made it harder to trace them, Reuters reported.
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