Construction work is under way on the dam, which would be Africa’s second largest hydro-electric dam, providing some 1,800 megawatts of electricity.
But one of the groups, International Rivers, says the government still needs about $1.4bn (£930m) to finish it.
“Gibe III is the most destructive dam under construction in Africa. The project will condemn half a million of the region’s most vulnerable people to hunger and conflict,” said Terri Hathaway, director of International Rivers’ Africa programme.
The dam would flood a huge area, creating a 150km-long lake and preventing people from planting their crops on the river’s flood plains, as they have done for many generations.
Campaigners also fear that the dam would reduce the flow of water into Lake Turkana, which some 300,000 people depend on.
However, Ethiopia’s government disputes that the overall amount of water would change – they say it would just be a more regular flow throughout the year.
Tewolde Gebre Egziabher, head of Ethiopia’s Environmental Protection Authority, told the BBC the project was “very sensible”.
“The advantages for the whole country, the local communities around, even for our neighbouring countries – including Kenya -so much more outweigh the small problems that will be caused on an immediate basis but are not long-lasting.”