FIA president Jean Todt says he wants to keep "political debate" out of Formula 1.
Ecclestone has now hit back in the pages of British newspapers, declaring: "Lewis, you state that I am uneducated and ignorant. I have the same level of schooling as you.
"At least I had a reason - I was at school during the last war, not always under the best conditions. You are lucky because if I had been properly educated perhaps Formula 1 would not be as it was for you to benefit as you have.
"Don't think about what your skin colour is - think about what colour your mind is. Don't envy others. Just improve and catch up," the 89-year-old said.
FIA president Todt revealed to AFP France that he had a "long chat" with Hamilton in the wake of the six-time world champion's latest critical comments.
"I have a lot of time for anyone with a calling, a commitment, and I think it's great when a leader in their field wants to get involved," said the Frenchman.
"And we at the FIA have been involved for a very long time in diversity, gender equality - provided it is not a political debate.
"Our organisation is apolitical, like the Olympic Committee, with whom we work very closely. I totally agree that sport is a good platform, and in Formula 1 we gave the opportunity to those who wanted to express themselves," Todt added.
He is referring to the controversial and Hamilton-inspired 'take a knee' moments that have been occurring before the races in the spectator-less corona era.
Hamilton, 35, has said he would like to convince those of his rivals who choose instead to stand.
Todt said: "There are some who may want to kneel down, there are some who may not want to express themselves in the same way. It's freedom, it's democracy, and we must ensure that those principles are absolutely respected."