The AUC is on Washington's list of terror groups
Colombia's right-wing paramilitary leaders have called on the government to allow them to address Congress.
The United Self-Defence Forces of Colombia (AUC) said it wanted parity with left-wing ELN rebels, whose leader recently spoke to the Senate.
The demand by the AUC came after the authorities said formal peace talks with the group had been postponed.
The talks had been scheduled to start on Tuesday in a special zone in the northern province of Cordoba.
The government aims to demobilise the AUC, believed to number at least 13,000 fighters, by 2006.
However, the peace process has been faltering for some time.
In May, paramilitary commanders agreed to move to the zone in Cordoba under the supervision of the Organisation of American States.
On Tuesday, the government said both sides had agreed to postpone the start of formal talks, in order to allow more time to deal with security concerns and logistical difficulties.
Under the AUC's latest proposal, four of their commanders - still to be named - would travel to Bogota to appear before Congress.
The AUC said it decided to make the request after jailed ELN guerrilla leader Francisco Galan was allowed out of prison for one day on 4 June to meet top government officials, address the Senate and discuss a renewal of peace talks.