Accrington Stanley chairman Andy Holt has accused the Premier League of "destroying the game," with the organisation responding by asking if he wanted it "to continue the support" provided to his and other Football League clubs.
In a series of tweets, Holt accused the league of allowing huge amounts of wealth to accumulate at the top end of English football.
A Premier League statement said the organisation would be writing to him to ask if he wanted it "to continue the support" provided to his and other Football League clubs.
It added: "The Premier League supports all clubs in the EFL with solidarity payments and provides significant funding for their community projects and youth development schemes -- all things that Accrington Stanley benefit from.
"It is only because of the interest in our competition and in Premier League clubs that we can support Accrington, the wider football pyramid, and communities and schools across the country."
But Holt hit back, tweeting: "Make whatever threats you like, it is and will still be my opinion. Take whatever action you see fit, over and out."
- Andyh (@AndyhHolt) 9 May 2017
He had been commenting on newspaper reports claiming that Zlatan Ibrahimovic is paid over £350,000 a week by Manchester United, and that agent Mino Raiola had pocketed £41 million from the deal that brought Paul Pogba to Old Trafford.
He wrote: "Hang your heads in shame @premierleague, you are an absolute disgrace to English football" and said the financial imbalance was "ruining the pyramid and @England national team."
Holt added: "You're destroying the game, not 'rogue' owners."
The Accrington chairman pointed out that the annual budget at his League Two club was almost 20 times smaller than the fee reportedly paid to Raiola.
"The cash paid to this agent is almost double the funding for all the @EFL @SkyBetLeagueTwo clubs put together. WAKE UP @premierleague.
"The @EFL is like a starving peasant begging for scraps off your table @premierleague. Owners might ruin clubs, but you're destroying the game."
After receiving the Premier League's letter, he responded by writing: "Speaking personally, @premierleague, I now understand @EFL predicament in trying to negotiate and have constructive discussions with you.
1. Speaking personally .@premierleague £41.39m to an agent for 1 player in your league is obscene whist bottom of pyramid is struggling.
- Andyh (@AndyhHolt) 10 May 2017
"To threaten funding to @ASFCofficial + 71 other @EFL clubs is breathtaking. You are out of touch. £41.39m to an agent for 1 player in your league is obscene whist bottom of pyramid is struggling."
He wrote: "Yesterday I had the temerity to criticise the Premier League for the disgraceful largesse with funds, transfer fees, agent fees that TV money has allowed to get out of control.
"I said they should hang their heads in shame at the £41,390,000 allegedly paid to agents in the transfer of Paul Pogba to Manchester United.
"I did not say that anything illegal or improper took place. I did say that the Premier League should be ashamed about this largesse when the pyramid is so stretched outside the top tier.
"In response to my comments the Premier League threatened to stop any funding for EFL clubs. I class this as a threat too far.
"My personal response is that they can please themselves with their funds. However, I do not speak for the EFL or its member clubs. I do stress it's my personal opinion."
PA Sport reported that Accrington and each League Two club would receive £430,000 in solidarity payments from the Premier League this season.
The payments are linked to the value of the Premier League's broadcasting rights, with League One clubs getting £650,000 each and Championship clubs £4.3m.