Interpol issued an international arrest warrant for the younger Diack this month, adding that French judicial authorities are seeking to prosecute him.
"We will not extradite a Senegalese. Those are the instructions the president (Macky Sall) gave the government," Prime Minister Mahammad Boun Abdallah Dionne said in parliament on Thursday. "But that does not mean he has the right to impunity."
As president of one of Africa's most stable French-speaking democracies, Sall enjoys close relations with former colonial rulers. A presidency spokesman was not available for comment.
Diack's son Papa and two Russian officials have been banned from athletics for life by an IAAF ethics board for covering up an elite Russian athlete's positive dope test and blackmailing her over it. The family call the allegations "excessive and insignificant".
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The IAAF scandal coincides with a corruption scandal shaking world soccer governing body FIFA that has resulted in bans and arrests around the world.
(Reporting by Diadie Ba, Writing by Emma Farge, Editing by Angus MacSwan)
