Noboa, a former legislator and son of one of the country's richest men, took office in November on promises to fix the struggling economy and stem a wave of violence on the streets and in prisons which has been growing for years.
Noboa declared the 60-day state of emergency- a tool used by his predecessor to little success - on Monday, enabling military patrols, including in prisons, and setting a national nighttime curfew.
The measure was a response to the disappearance of Adolfo Macias, leader of the Los Choneros criminal gang, from the prison where he was serving a 34-year sentence, and incidents at six prisons, including hostage-takings of prison guards.
Police and prosecutors have given scant information about Macias' disappearance.
Three police officers working the night shift were taken from their station in the southern city of Machala, the police said on social media on Tuesday, while a fourth missing officer was taken by three criminals in Quito.
"Our specialized units are active with the goal of locating our colleagues and proceeding with the capture of the perpetrators," the police said. "These acts will not remain in impunity."
The explosions, including on a pedestrian bridge Quito, resulted in no injuries, but the capital's municipal authority asked in a statement for reinforced security amid the "unprecedented" crisis.
Noboa has said he will not negotiate with "terrorists" and the government has blamed recent incidents of prison violence on Noboa's plan to build a new high security prison and transfer jailed gang leaders.
Prisons agency SNAI has given no information about the guards who are being held hostage.
Noboa plans to hold a plebiscite focused on security efforts.
(Reporting by Alexandra Valencia in Quito; Writing by Julia Symmes Cobb; Editing by Tomasz Janowski)
