Michael Findley and Olatunji Denbow are pleading with the Prime Minister and the Director of Public Prosecutions to have their court matters expedited.
The two men remain at large, having escaped the Golden Grove Prison almost one week ago.
Yesterday, even as the search for them continued, the men issued a video statement saying they pose no threat to anyone.
The two are among five people arrested and charged with the double murders of Andre La Touche and Abiola Noel in 2016.
In the video statement, the two men slam a witness whom they claim has been making false statements, not just in their cases but others as well.
Mr. Denbow says they want their cases to be handled swiftly.
Yesterday Prisons Commissioner Gerard Wilson called on the men to let better sense prevail and turn themselves in.
And Police Commissioner Gary Griffith believes people wearing shit and ties are helping the men while they are on the run.
The Commissioner says he will pursue them with the same energy as with the others who have been recaptured.
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