The guerrilla movement -- the last of its type still fighting government forces in Colombia -- asked the government late on Tuesday to "agree a bilateral 90-day ceasefire" in response to a call from the United Nations to reduce violence and conflicts during the coronavirus pandemic.
"Our Dialogues Delegation that is in Havana is empowered to process all the operational details," said the ELN in a statement.
The offer received short shrift from Duque, who wrote on Twitter: "I will never stop complying with the constitutional duty to confront criminality throughout the territory," adding that the ELN is a "terrorist group."
"Colombia demands that they free the hostages and put an end to their criminal acts."
The ELN suspended its operations during April and asked Duque to return to the negotiation table to discuss a bilateral ceasefire, but said that was ignored.
The coronavirus has infected 124,000 Colombians and left 4,300 dead.
The rebels said a truce "would create a climate of humanitarian detente" conducive to restarting peace talks that have been suspended since the ELN carried out a bombing on a police academy in January 2019 that left 22 recruits dead.
Duque has said he will only return to the negotiating table if the ELN releases all hostages and stops "criminal activities."
The ELN has refused arguing that such conditions are one-sided.
Formed in 1964, the ELN is believed to comprise about 2,300 fighters and operates in about 10 percent of the country.
Since the historic 2016 peace accord that turned Revolutionary Armed Forces of Colombia (FARC) rebels into a communist political party after a half century of armed conflict, the smaller ELN is considered the last active guerrilla group in the country.