The National Liberation Army, ELN, is considering a temporary ceasefire with the Colombian Government before September.
The rebel leader Pablo Beltran said any truce would depend on the commitments reached by both parties.
Beltran also said that although differences remain, they will discuss them at the negotiating table.
He said the majority of the third round of talks, which began on July 25, have focused on finding a way forward.
However, the head of the government delegation, Juan Camilo Restrepo, said that "the ELN has not begun to talk about technical aspects of a possible ceasefire and much less deadlines."
According to Restrepo, the government wants the ELN to stop kidnappings and attacks before it will implement a bilateral ceasefire.
The ELN's main concern is the vacuum in areas vacated by the Revolutionary Armed Forces of Colombia after they signed a peace deal with the government last November.
The rebels say right-wing paramilitary groups are now taking over.
Beltran said "This is very difficult, because there are very serious situations against these communities, and that is where the murder of social, environmental and human rights leaders is happening."
He added that the ELN has asked the Colombian government to commit itself "to neutralize this massacre of leaders, because for us there is already a genocide similar to the one that happened with the Patriotic Union, UP, 30 years ago."
The UP was a party created by leaders of the FARC-EP and various leftist groups during an unsuccessful round of peace talks with the government.
Members of the UP were the targets of a systematic campaign of assassination
5,000 members and supporters were killed by right-wing paramilitary groups, often working with state backing.
However, the ELN's chief negotiator said he is "optimistic" that the latest talks will make progress.
The parties will be able "to unlock the difficulties we have and in that short time I think a concrete cease-fire agreement is possible," he said.