The 32-year-old paceman was banned earlier this month for breaching the players' code of conduct by publicly criticising the Pakistan Cricket Board (PCB) after he was not offered a central contract in January.
The three-member tribunal, headed by retired judge Aftab Farrukh, met here Monday and will meet again on Wednesday to take a decision on the maverick Akhtar's appeal.
"After arguments from both sides, Akhtar voluntarily asked to tender an unqualified apology to all the public, the chairman of the PCB and all his teammates for his actions," Justice Aftab said.
Akhtar lashed out at the PCB in January after he was dropped from the list of 15 contracted players, following Pakistan's 1-0 defeat against arch rivals India a month before.
He was already on two-years' probation for hitting teammate Mohammad Asif with a bat a few days before the Twenty20 World Cup in South Africa in September last year.
A statement read by Akthar's lawyer said: "I (Akhtar) would like to apologise from the bottom of my heart for any grief or embarrassment that may have been caused to the nation, particularly to the PCB chairman Nasim Ashraf.
"I have resolved to alter my habits to refrain from such incidents in future and I will obey the PCB rules and regulations," the statement said.
Justice Farrukh said the tribunal will now wait for the PCB's response.
"Though Akhtar's apology has made the case easier to decide, we have to see what is the PCB's response. His apology may bring a mitigation factor in the case. The punishment may be reduced or it can be increased too," Justice Farrukh said.