His comments have widely been interpreted to be a dig at former president John Mahama who in 2015 said presidential aspirants in the 2016 elections, including Mr Akufo-Addo, have no right to criticise him because they have not held the position before.
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Speaking Saturday at the University for Development Studies in Tamale, president Akufo-Addo said: "I am sure you have seen and heard some of the presidential aspirants of the leading opposition party taking jabs at my government in order, ostensibly, to prop up their campaigns. And, whilst at it, they desperately trying to get me to respond to them.
"Let me state here and now, for the record, president Akufo-Addo will not respond to presidential aspirants. He will respond to presidential candidates that have been duly elected by their parties.
"Then, he will engage those who think Ghanaians have short memories."
His comments mirror a similar one former president John Mahama made in 2015 when the then opposition New Patriotic Party called him "incompetent" and he responded by saying they can't criticise him because they have never been president before.
At the time, then candidate Akufo-Addo and his running mate, Dr Mahamudu Bawumia, led the onslaught against Mr Mahama, calling him "incompetent."
In an angry tone, Mr Mahama responded saying he would only take criticism from ex-presidents Rawlings and Kufuor because they have been governed Ghana before.
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He said: “They [NPP] have told all their communicators anytime you mention Mahama or NDC say incompetent. I hear Bawumia and co say incompetent Mahama administration. You never held any responsibility anywhere near presidency before. You do not know what it is like to be President.”
“I will take that word from Kufuor or Rawlings because they have been there before. All of you guys have never ever come near the presidency and you stand there and say incompetent Mahama administration… What do you know about competence?”