Faye, his prime minister Ousmane Sonko, and several of their party members were imprisoned during the presidency of former leader Macky Sall.
They have repeatedly denounced the manipulation of the justice system over the past three years, and campaigned on a promise of in-depth reforms.
Faye on Tuesday spoke of the need to carry out a "profound overhaul" of Senegal's justice system, citing the recent unrest that has shook the West African country.
"The problem and urgency (of reforming the justice system) calls out to all of us, above and beyond any partisan considerations," he said.
The consultations represent the fourth edition of the "national dialogue" — an initiative originally introduced by Sall — and bring together industry professionals, university professors, and members of the opposition and civil society.
The meetings are due to run until June 4 in a conference center in the new town of Diamniadio, near the capital Dakar.
Faye said participants will discuss issues such as the length of criminal trials, detention conditions, and preparations for the social reintegration of prisoners.
The conclusions are then due to be submitted to him on June 4.
"The purpose of this exercise is to help us pave the way for a pragmatic reform of our justice system so that it is more inspiring to those who come before it and preserves its dignity," Faye said.
"I would particularly like to emphasize that we are not opening an inquisitional trial here to point the finger of blame at one or more guilty parties to be thrown out," he added.
Faye also warned against a desire to "build a republic of judges," which he said would call into question "the cardinal principle of our democracy."
Senegalese authorities last week launched an online platform for citizens to post their views on judicial reform to be added to the meeting.