"It is known that thousands more have been denied access to the civil registry in the first place," said Canton, former executive secretary of the Inter-American Commission on Human Rights.
He also repeated earlier criticism of the ruling itself. "It doesn't matter whether you discriminate against 24,000 or 100,000, it is still a blatant case of discrimination and arbitrary conduct," he said.
Canton said the government should publicly recognize that the court decision is racist and that it violates international agreements.
Activists say most of those affected by the court ruling are the descendants of poor migrants who came to work in sugar cane fields from neighboring Haiti, a predominantly black nation that shares the island of Hispaniola with the Dominican Republic.
Rosario said more than half of the 24,392 residents not properly registered are of Haitian descent.
Thursday's announcement comes after the Constitutional Court ruled in September that people born in the Dominican Republic to parents who were neither citizens nor legal residents are not automatically entitled to citizenship under the constitution adopted in 2010. The decision was retroactive, applying to anyone born after 1929.
Officials have said they would not deport or expel anyone just because they are not properly registered with the government.
"If they prove they have roots here, if they prove they were born in this country and have not violated any laws, their documents will be put in order," Rosario said.
The government says, however, that anyone who can't do that will be stripped of their Dominican birth certificate and identification card, known as a cedula, which is issued at age 18 and allows participation in public activities ranging from voting to holding a job.
The Electoral Council now has one year to review in detail each of the 24,392 cases. Officials have not yet set a deadline for those affected to prove their citizenship, which human rights activists say has become increasingly difficult because of government actions in recent years.
In 2007, the Electoral Council ordered the denial of citizenship documents to all children born to migrants living illegally in the Dominican Republic, and authorities confiscated the papers of people who already had their documents.
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Associated Press writer Dionisio Soldevila reported this story in Santo Domingo and AP writer Danica Coto reported from San Juan, Puerto Rico.