The 53-year-old's comments came during a radio interview in his homeland earlier this week as he launched a stinging attack on Aguero following the Manchester City striker's split with wife, Giannina - Maradona's daughter.
The pair - who have a son, Benjamin, together - parted earlier this year after a four-year marriage, with Maradona saying: "He's a wimp who I don't even want to name."
However, Aguero has now attempted to diffuse the situation with a statement on his official Facebook page.
He wrote: "It always has been very clear in my mind that Benjamin is the most important part of my life, he comes before anything else. I have never been willing to publish my private life in (the) media.
"That's why I spoke with my people, telling them that, regardless of how offended they might be, they shouldn't answer any questions (to the media).
"I have never spoken about these matters, and this is the last time I will do it. I hope every party involved understands this the same way.
"For all of our sakes, especially Ben, we need to solve this privately. This is the way I've always done this, this is the way I'll carry on doing this."
Aguero has made eight Premier League appearances for City this season, scoring seven times, including in the 2-1 defeat to title rivals Chelsea last weekend.
