The government yesterday received photos from the Colombian TV station RCN suggesting the three had been killed.
The journalists were abducted by rogue forces of Colombia's FARC guerrillas along the countries' shared border on March 26.
President Lenin Moreno, in an emotional speech, said if the government does not receive word on the team's status "we will move forcefully ... not hesitating to punish these human rights violators," the president said.
"The clock starts clicking right now," Moreno said.
On April 3, Colombia's RCN television aired a 23-second video showing the trio wearing chains with locks around their necks, the first proof of being alive.
One of the hostages asked Moreno to reach an agreement for their release.
Moreno in turn announced his government "will do everything possible and impossible so that they return safe and sound," according to a spokesman.
Moreno decided to return urgently to Quito after a Colombian television channel announced it had received photographs that show the three journalists may be dead.
The journalists were on assignment in the border area where Ecuadoran security forces have come under a series of deadly attacks blamed on rogue FARC elements involved in drug trafficking.
The larger FARC movement reached a historic peace agreement with the Colombian government in 2016.
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