A week after a massive quake struck Nepal, authorities have officially ruled out finding any more survivors even as thousands are still unaccounted for.

The official death toll stands at 6,620, and the number could rise sharply as more bodies are being pulled out from the debris.

"We are trying our best in rescue and relief work but now I don't think that there is any possibility of survivors under the rubble," Home Ministry spokesperson Laxmi Prasad Dhakal told AFP.

The focus of the relief operations has now shifted to remote rural areas which are badly affected by the 7.9 magnitude quake. Rescue workers are still unable to reach some parts of Nepal, one of Asia's poorest nations.

European authorities have said at least 1,000 European nationals are missing.

"EU nationals unaccounted for – there are 1,000 – but that of course doesn't mean that they're dead, just that they haven't reported back. So 1,000 unaccounted for EU nationals. But we don't know what is happening to them, whether some of them are dead, or some of them have just not reported, but that is the latest figure," Rensje Teerink, the chief of the EU delegation in Nepal, told reporters.

Many of the European backpackers are thought to have been on popular trekking routes in the Himalayas when the killer quake struck.

Meanwhile, workers are quickly cremating unclaimed bodies so as to avoid epidemics. Fears of diseases breaking out have heightened as medical workers are running short of clean water and toilets.