ICC chief Dave Richardson made the call after Butt and Asif had appeals against their minimum five-year suspensions for spot-fixing dismissed by the Court of Arbitration for Sport last week.
The duo were banned by the ICC after they were found guilty, along with Mohammad Amir, of being a part of a plot to bowl no-balls during the Lord's Test against England in 2010.
Amir has since admitted his guilt, however, Butt and Asif have expressed their innocence.
However in CAS's written statement it was stated that former Pakistan captain Butt - described as the orchestrator of the plot during a criminal case that resulted in all three players being jailed - had admitted his role.
Given that admission Richardson believes now is the time for both to publicly apologise and aid the ICC's investigations into the matter.
"The guilt of these men has now been established on three separate occasions, in three separate sets of proceedings and in three separate forums," Richardson said in a press release.
"The time has now come for them to stop misleading the members of the public, especially the supporters of the Pakistan cricket team, and to publicly accept their parts in this corrupt conspiracy.
"In addition to the CAS finding Mr Asif a party to the conspiracy to act corruptly, it is also pleasing to note from the decisions that Mr Butt acknowledged his part in the fix before the CAS panel. I would urge them to start the process of rebuilding their lives and reputations by apologising for their actions and meeting with ICC's anti-corruption officials to come clean."
Butt had asked CAS to reduce the length of his ban, while Asif was appealing against the verdict itself. Neither persuaded CAS of their case, though, with Butt left to his 10-year ban (with five suspended) and Asif to his seven-year ban (with two suspended).
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