The anti-doping authority has told players, who originally were given 10 days in which to respond, they now have until July 11.
ASADA announced last week that the players were required to show why they should not be issued infraction notices over the alleged use of the peptide thymosin Beta 4.
On Wednesday the players threatened legal action if they weren't granted a stay until Essendon's Federal Court case against the joint ASADA-AFL inquiry into the club's 2012 supplements program was completed.
The players are also seeking access to ASADA's evidence so they can decide on their next move.
It's not clear whether ASADA has responded to these requests at this stage.
Legal action launched by the Bombers and suspended coach James Hird is due to begin in the Federal Court on Friday 27 June.
Having initially refused to confirm the extension to AFL.com.au on Thursday afternoon, ASADA issued a fresh statement later in the day.
"ASADA CEO, Ben McDevitt, confirms he has granted an extension of time to allow 34 Australian Football League (AFL) players to submit responses to show-cause notices," the statement read.
“Players will have to 11 July 2014 to lodge their submissions."
