Last year, a majority of Ecuadoreans voted to shutdown the 43-ITT block to protect the Yasuni reserve in the Amazon, while the country's top court granted one year for the removal of oil infrastructure in the region.
Noboa recently floated the idea of postponing the block's closure, citing resources needed to finance a military offensive he declared earlier this month to tackle criminal gangs he has called terrorists amid spiraling violence.
State-owned Petroecuador has previously said that closing the block - which produces some 55,000 barrels of oil per day - could begin in August.
"If the president signs a document stating he won't comply with the will of the people(...), then the Constitutional Court will have to remove the president, we will take charge of pushing criminal charges," Pedro Bermeo, from environmental advocacy group Yasunidos, which pushed the referendum, told journalists.
During the same press conference Leonidas Iza, president of Ecuador's largest Indigenous group, CONAIE, threatened to take the case to both Ecuador's top court and the Inter-American Commission on Human Rights (IACHR) if need be.
"Democrats respect the will of the people," Iza said. "Opportunists take advantage of the will of the people for their own ends. President Noboa is at the point of revealing whether he is an opportunist or a democrat."
The government did not respond to requests for comment.
Closing the block could cost Ecuador some $13.8 billion over the next two decades and will result in the loss of 12% of the country's oil output, which averages about 492,000 bpd, according to Petroecuador.
(Reporting by Alexandra Valencia; Writing by Oliver Griffin; Editing by Marguerita Choy)
By Alexandra Valencia