Two former commanders from the group - known by their aliases Ivan Marquez and Jesus Santrich - appear in the 32-minute YouTube video announcing the new offensive, which Marquez said was filmed in Colombia’s Amazon.
"This is the continuation of the rebel fight in answer to the betrayal of the state of the Havana peace accords," Marquez, dressed in olive fatigues and surrounded by armed fighters said. "We were never beaten or defeated ideologically, so the struggle continues."
Marquez was a key negotiator of the peace agreement signed in 2016. He went missing last year after his nephew was arrested and taken to the United States to cooperate with drug-trafficking investigators.
The announcement comes amid severe challenges for the complex accord, including the murder of hundreds of former rebels and human rights activists, delays in funding for economic efforts by ex-combatants, and deep political polarization.
President Ivan Duque was elected on a platform to change parts of the deal, but has failed to get congressional or judicial support to do so. He has repeatedly said former guerrillas with a true desire to disarm will be supported.
"The great majority remain committed to the deal, despite all the difficulties and dangers," former FARC commander Rodrigo Londono, known as Timochenko, said on Twitter. "We are with peace."
Londono is now a leader within the Revolutionary Alternative Common Force, the FARC political party born out of the peace accord.
There was no immediate reaction from the government.
"All of this, this trick, this betrayal, this perfidy, the unilateral modification of the text of the accord, the unfulfilled commitments on the part of the state, the judicial set-ups and insecurity, have obliged us to return to the mountains," said Marquez, whose birth name is Luciano Marin.
The group will seek to coordinate with fellow leftist rebels the National Liberation Army (ELN), Marquez said, and will not use kidnapping and ransom as a source of financing.
Security sources said the force commanded by Marquez could reach 2,200 fighters.
Santrich, whose birth name is Seuxis Pausias Hernandez, is wanted in extradition by the United States for alleged conspiracy to export 10 tonnes of cocaine.
The commander Hernan Dario Velasquez, who goes by the alias "El Paisa," also appears in the video.