"I challenge you to a charity fundraiser - one on one individual 1/4 ironman or a 1/2 marathon (or longer if you prefer, I'm keen)."
Mr Flavell suggested they do it as a fundraiser and money go to families in Edgecumbe who were affected by the recent floods.
Mr Coffey, 37, said he did not initially know what Mr Flavell was responding to.
He subsequently discovered his sister had posted a comment on the sitting MP's age, suggesting it was time he retired.
"I've never attacked him on his age," Mr Coffey added.
Mr Coffey posted a response on Facebook suggesting a debate instead.
"Thank you for your wero and offer," he wrote.
"To clarify it is not your age that me and Labour say hinders your capabilities, rather your ability to deliver for all Maori especially here in Waiariki.
"While I thank you for the invite, I'm sure you will agree that our people won't be any wiser on who to vote for by us competing in a random sports event.
"But I love a good challenge so I want to whakahokia te wero by challenging you to a debate. It's what politicians do isn't it?"
Mr Coffey said he believed a debate would be more suitable than a "random sporting event".
Matua Te Ururoa Flavell MP Te Ururoa Flavell! Thank you for your wero and offer. To clarify it is not your age that me...
Posted by Tamati Coffey - Labour MP for Waiariki on Sunday, 14 May 2017
"I've run about eight half-marathons ... I'm not afraid of half-marathons or going for a run."
The issue Mr Coffey proposed to debate was the new Te Tura Whenua Maori bill, which was introduced by Mr Flavell and aimed to reform Maori land law.
He proposed charging an entry fee to the debate of $10, with the proceeds going to Edgecumbe.
Mr Flavell has since posted a response on his Facebook page suggesting he and Mr Coffey do both challenges.
Mr Coffey said Mr Flavell had "kind of changed the game completely" with his alternative suggestion.
"I definitely don't want to do the race ... there's real issues out there.
"I'm still focused on having a debate. If anything, I'm more determined to."