The former Tory MP, 67, defeated UKIP Wales leader Nathan Gill to lead the party's seven-strong assembly group.
Mr Farage said he was "not particularly in favour of Mr Hamilton's return to the front line, aged nearly 70".
Mr Hamilton replied: "If Attenborough can still survive in a jungle of wild animals and predators at 90, I'm sure I'll be fine in the assembly."
Mr Farage, who is 15 years younger than Mr Hamilton, had described the treatment of Mr Gill as "an act of deep ingratitude" after UKIP won its first seats in the assembly.
Speaking about Mr Hamilton on LBC radio on Friday, Mr Farage said: "I think it is difficult to return to frontline politics after a 20-year gap when you are getting on a bit in years.
"But there you are, perhaps he'll surprise me."
He added: "One thing I will say, he is utterly committed to this EU cause, and he has been since the 1960," referring to Mr Hamilton's opposition to UK membership of the European Union.
In response, Mr Hamilton said: "The average UKIP member will be very disappointed at Nigel's ageist remark.
"UKIP has many thousands of active and vigorous senior members.
"It seems particularly odd to knock old age at the very moment we celebrate the 90th birthdays of two icons of Britishness - Her Majesty the Queen and Sir David Attenborough.
"If Attenborough can still survive in a jungle of wild animals and predators at 90, I'm sure I'll be fine in the assembly.
"Clement Atlee was 65 when, as Prime Minister, he introduced the NHS.
"Churchill was 72 when he led us to victory against the Nazis.
"Ronald Reagan was 77 when he brought about the collapse of the Soviet Union and ended the Cold War.
"Is Nigel suggesting he could have done a better job than any of them, because he is 15 years younger than me?"
Among those who supported Nathan Gill in the leadership vote last week was Mark Reckless, a former Conservative MP and now a AM for South Wales East.
Asked what the relationship between Mr Hamilton and Mr Gill was like, Mr Reckless said: "Not good."
"I hope over time wounds will heal and we'll want to do the best for the people who voted for us and Wales as a whole," he told BBC Wales on Thursday.
Mr Reckless said he had supported Mr Gill in the leadership challenge, but added: "I accept the result."
Of Mr Hamilton's bid to go for leader, Mr Reckless said: "It's not what I would have done, but we are where we are.
"I don't want to say anything critical about Neil on that."
Neil Hamilton has rejected suggestions by UKIP leader Nigel Farage that he is too old for frontline politics.