In a radio interview on Monday, Noboa also said that a "technical analysis" was needed before the incident could be called an enforced disappearance -- despite prosecutors saying it was being investigated as an illegitimate use of force.
Dozens of people protested in the capital Quito and the southwestern city of Guayaquil to call attention to the case.
"They were taken alive, and we want them back alive," said Luis Arroyo, father of brothers Josue and Ismael, who disappeared in Guayaquil on December 8 along with their friends Saul Arboleda and Steven Medina.
Demonstrators in both cities carried signs reading "Where are our children?" and "Black children are not criminals."
Many Ecuadorans suspect soldiers kidnapped the four boys, who are aged between 11 and 15 and went missing two weeks ago while they were out playing football.
Arroyo told the TV channel Ecuavisa he received a call from a man who put one of his sons on the line.
The boy said that soldiers had abruptly arrived, firing in the air and forcibly taking them, and that they had been beaten.
Noboa, on the social media platform X, on Sunday said: "I have ordered the intensification of all actions necessary to locate the four children and to find those responsible so they answer for their acts."
Ecuador's joint chief of staff, Admiral Jaime Vela, "ruled out... any involvement" of military personnel in the boys' disappearance.
Vela said the armed forces would not interfere in the investigation "nor will they cover up any event."
Defense Minister Gian Carlo Loffredo has attributed the boys' disappearance to "criminal groups" and alleged the case was being used for "political interests."
The disappearance has sparked widespread indignation in Ecuador, where kidnapping, extortion and murders are now commonplace.
Noboa, 37, is the US-born and -educated heir to a banana fortune, and is seeking to win a four-year mandate in February 9 general elections.
He is currently serving out the final months of the term of his predecessor Guillermo Lasso, who called an early election to avoid impeachment.
Noboa has boosted the use of security forces to battle powerful drug gangs in Ecuador and sworn to turn back the tide of violence engulfing the once-peaceful South American country.
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