The ultimatum was issued late on Thursday by President Lenin Moreno, who gave the kidnappers until 11:00 am (1600 GMT) to give an answer after his government received photos from a Colombian TV station suggesting the trio, all Ecuadorians, were dead.
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"Failing that, we will act with all forcefulness ... not hesitating to punish these violators of every human right," said Moreno, who was close to tears.
"The clock starts clicking right now," he said, in remarks at Quito airport as he cut short a visit to a Lima for the Americas Summit which was to begin on Friday.
Ecuadoran experts examined the photos but were unable to confirm their authenticity.
Reporter Javier Ortega, 32, photographer Paul Rivas, 45, and their driver Efrain Segarra, 60, were kidnapped on March 26 by rogue forces affiliated with Colombia's recently-disbanded FARC rebels.
The team, from Ecuador's influential El Comercio newspaper, was abducted while on assignment along the border between the two countries, where Ecuadoran security forces have come under attack by former FARC rebels who are still active in drug trafficking.
Moreno was already in Lima when the photographs emerged, prompting him to urgently return to Quito to handle the crisis.
Both he and his Colombian counterpart Juan Manuel Santos have agreed to wait for contact from the kidnappers before taking "forceful" action.
With the deadline looming, Moreno was huddled in crisis talks with his cabinet as a top-level delegation was flying over from Bogota, led by Colombian Defense Minister Luis Carlos Villegas who was accompanied by top military and police officials.
Ecuador's Communications Minister Andres Michelena said the delegation would be involved in preparing "joint operations," without giving further details.
'Stop helping Colombia'
On April 3, Colombia's RCN television aired a 23-second video showing the trio wearing chains with locks around their necks, in what was the first proof of life.
One of the hostages appealed to Moreno help secure their release.
In response, the government pledged to do "everything possible and impossible so that they return safe and sound," a presidential spokesman said.
In the video, the unidentified captors said they would release the hostages if Ecuador stopped helping Colombia fight the insurgents.
The journalists' kidnapping has alarmed and unsettled Ecuador, with media saying it was the first such abduction in the country in three decades.
According to the Ecuadoran military, the dissident group believed to be behind the abduction is led by a rebel called "Guacho", an Ecuadoran in his 30s who had served as a rebel in the FARC for 15 years, specializing in explosives, drug smuggling and financing.
The group is thought to number 70 to 80 people and is involved in cross-border drug trafficking through the jungle.
A 2016 pact between the Colombian government and the FARC ended half a century of armed conflict, saw 7,000 rebels disarmed and the ex-rebels transform into a political party.
However, some 1,100 guerrillas broke away from the agreement, primarily to pursue drug trafficking and illegal mining, according to the Colombian government and independent research centers.
The FARC has long been active in the remote Ecuador-Colombia border region.
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