Ecuador's president has ordered that criminal gangs be "neutralised" after days of violence culminated in an attack on a television studio.

Masked gunmen broke into public television channel TC's live studio during a broadcast, forcing staff to the floor.

Police made 13 arrests following the attack, which injured two employees.

At least 10 people have been killed since a 60-day state of emergency began in Ecuador on Monday.

The emergency was declared after a notorious gangster vanished from his prison cell. It is unclear whether the incident at the TV studio in Guayaquil was related to the disappearance from a prison in the same city of the boss of the Choneros gang, Adolfo Macías Villamar, or Fito as he is better known.

President Noboa said on Tuesday that an "internal armed conflict" now existed in the country and he was mobilising the armed forces to carry out "military operations to neutralise" what he called "transnational organised crime, terrorist organisations and belligerent non-state actors".

In neighbouring Peru, the government ordered the immediate deployment of a police force to the border to prevent any instability spilling over into the country.

The US has said it condemns the "brazen attacks" in Ecuador and is "co-ordinating closely" with President Daniel Noboa and his Ecuadorean government and stands "ready to provide assistance".

Ecuador is one of the world's top banana exporters, but also exports oil, coffee, cocoa, shrimps and fish products. A surge in violence in the Andean nation, inside and outside its prisons, has been linked to fighting between drug cartels, both foreign and local, over control of cocaine routes to the US and Europe.

During Tuesday's assault at the TV station, one gunman pointed a pump-action shotgun at the head of one of the captives, who was also threatened with a revolver.

A woman could be heard pleading, "Don't shoot, please don't shoot," AFP news agency reports, while a person could be heard screaming in apparent pain.

"Please, they came in to kill us," a TC employee told AFP in a WhatsApp message. "God don't let this happen. The criminals are on air."

One cameraman was shot in the leg, and another's arm was broken in the attack, the deputy director of news said.

"Through our earpieces the producers told us, 'Be careful, they are trying to enter, they are stealing, they are mugging us'," Jorge Rendon told the Reuters news agency.

"The doors in the studio are very thick, almost bullet-proofed, and they were trying to get in because they wanted to gain access to the studio so we would say whatever they wanted us to say," he said.

Posting video of the suspects arrested on social media - and their weapons - police said the perpetrators would be "punished for terrorist acts".

President Noboa's emergency declaration responded to a wave of recent jail riots and escapes from prisons and other acts of violence blamed by authorities on criminal gangs.

His decree listed the Choneros (named after the town of Chone in Manabi Province) as well as 21 other gangs.

The order built on the state of emergency declared on Monday, which ordains a nightly curfew in an attempt to curb violence following Fito's escape. Security forces have been trying to re-establish order in at least six jails where riots broke out on Monday.

Eight people were killed and three injured in attacks linked to criminal gangs in Guayaquil on Tuesday while two police officers were killed by "armed criminals" in the nearby town of Nobol, police said.

In the city of Riobamba, nearly 40 inmates, including another convicted drug lord, broke out of a prison.

At least seven police officers were also kidnapped and a video circulating on social media shows three of the kidnapped officers sitting on the ground with a gun pointed at them as one is forced to read a statement addressed to President Noboa, AFP reports.

"You declared war, you will get war," the officer reads out. "You declared a state of emergency. We declare police, civilians and soldiers to be the spoils of war."

Police have ordered the evacuation of the government compound in Quito over security concerns.

Quito residents told Reuters news agency the city was in chaos since news of the attack at the TV station in Guayaquil.

"There's too much nervousness in the city," said Mario Urena. "At work, people are leaving earlier. All the people are leaving, you see a lot of traffic and alarms everywhere. There's a chaos."

Other people in the city of Cuenca told AFP of their shock at seeing the TV station seized.

"In Ecuador, we have never seen this kind of thing, where a channel has been practically hijacked and a broadcast starts with shootings, with kidnappings," said Francisco Rosas. "So what kind of security situation are we in? And if a television station is capable of receiving this type of robbery, this type of insecurity, imagine restaurants or shops."

In recent years, the country's prisons have been plagued by violent feuds between jailed members of rival gangs, often resulting in multiple massacres of inmates.

The Choneros are a powerful prison gang thought to be behind many of the deadly riots and prison fights which have erupted in Ecuador's jails over recent years.

Fito is thought to have absconded just hours before his planned transfer. Two prison guards have been detained on suspicion of helping him escape.

His escape is also a blow to the government of President Noboa, who was sworn in in November after winning an election tarnished by the assassination of presidential candidate and journalist Fernando Villavicencio.

Villavicencio had reported receiving death threats from Fito just days before he was shot dead while leaving a campaign rally in Quito.

Additional reporting by Vanessa Buschschlüter