Correa had accused Pachamama of participating in the physical harassment last week of Chile's ambassador and a Bielorussian businessman after they left a presentation on Amazon oil concessions.
In a Saturday TV appearance, Correa showed photos of protesters and fingered some as Pachamama members. The Interior Ministry accused the nonprofit via Twitter of "straying from its statutory objectives" and endangering "internal security and public peace."
Paez denied any Pachamama activists were involved in the harassment.
"What angers President Correa is that we are at the front lines in a conflict over this country's economic development. We oppose the expansion of the frontier of oil exploration into the Amazon," said Paez.
Her organization works closely with Achuar indigenous people, who oppose the exploration, said Patricia Usner, special projects director of the Pachamana Alliance, a San Francisco-based sister organization.
Pachamama means "Mother Earth" in the native Quechua and Quichua languages. The foundation says it has eight workers in Ecuador and an annual budget of $800,000 from donors including Germany, Finland, Norway, Holland, Italy and Belgium.
The protest last week followed the government's auction of 13 oil concessions in the provinces of Pastaza and Morona Santiago on the Peruvian border.
The nonprofits say they oppose the drilling because the government has not sought the approval of natives living in the region.
Correa has been at loggerheads with environmentalists since announcing in August plans to extract oil from the pristine Yasuni National Park. An initiative he announced in 2007 failed to persuade rich countries to pay Ecuador not to drill there.
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Associated Press Writer Frank Bajak contributed from Lima, Peru