The ELN, or National Liberation Army, said it "hopes" the government will attend peace negotiations that had been set for Wednesday in Ecuador's capital Quito.
It offered "to agree to a new and better bilateral ceasefire," it said in a statement read in Quito by its chief negotiator, Pablo Beltran.
President Juan Manuel Santos on Monday declared the suspension of the peace talks after three bomb attacks on police stations in Colombia killed seven officers and wounded dozens.
He also ordered his security forces to act with "maximum determination" against the rebel group.
Peace deal out of reach
The developments threatened to re-ignite an armed conflict that had been on the path to peaceful resolution following a historic November 2016 peace deal with Colombia's biggest insurgent group, the FARC.
A similar deal with the smaller ELN -- estimated to number 1,800 fighters -- has remained out of reach, however.
A previous ceasefire with the ELN expired on January 10 without any breakthrough, leading the government to say it was suspending talks.
The ELN then returned to targeting security forces and oil installations, and Colombia's military retaliated with an offensive resulting in dozens of deaths and arrests.
The three weekend bombings targeted police stations in three locations: two in the Caribbean port city of Barranquilla and one in Santa Rosa, in the department of Bolivar.
The ELN claimed responsibility for the worst of the attacks, which killed five officers and wounded 41 in Barranquilla on Saturday as police were assembling for roll-call.
Santos' government put the blame for all three on the ELN.
The United States condemned the attacks and another, apparently unrelated one, near the border in neighboring Ecuador that left 28 police and civilians wounded.
Tuesday's ELN statement did not refer directly to the bombings, but said the rebels were "responding to the military offensive."
'Gloomy' outlook
Santos, who won the Nobel Peace Prize in 2016 and who is due to step down in August after serving two mandates, had sought peace deals with the FARC and the ELN to end a half-century conflict.
His government opened talks with the ELN a year ago in Ecuador after reaching the peace agreement with the FARC, which has now disarmed and transformed itself into a political party.
But the ELN, unlike the FARC, has a federated structure with autonomous military units, which experts say makes a settlement more difficult.
"The scenario is really gloomy for a continuation of the negotiations," Camilo Echandia from the Externado University of Colombia told AFP on Monday.
Right-wing candidates in Colombia's upcoming election have urged the government to break off talks with the ELN entirely.