Fulham vice-chairman Tony Khan told a critical supporter who had urged him to leave the club to "go to hell".
Khan, 36, tweeted fans after Saturday's 2-1 defeat at Burnley, which left his side 19th in the Premier League, five points adrift of safety.
In a succession of messages he promised "multiple signings" in January but one fan replied: "Leave my club please."
Khan, the son of Fulham owner Shahid Khan, responded: "Never. I'll die at this club. Go to hell."
In explaining his response, Khan claimed the Twitter user telling him to leave had been critical in the past, including shortly after Fulham won promotion to the Premier League via the Championship play-offs in May.
The fan quickly denied he had been in touch after promotion and in turn said he was frustrated by the fact Khan splits his time with other roles at NFL franchise Jacksonville Jaguars and as president of All Elite Wrestling.
Signings promised as Khan calls for fight
Khan's online exchange began with him reacting to a defeat at Burnley in which the home side failed to register a shot on target yet ran out 2-1 winners courtesy of two own goals.
He wrote: "To the squad, staff and supporters, some people are waving the white flag and saying we should surrender. People said the same when we were six and four points behind during the past two seasons. We closed the gap both times.
"We can close this gap. It's on our players now to fight, finish and win.
"Our squad has great moments but they've shown their abilities more often than they've gotten the points we need.
"As with last January we'll make multiple signings to improve the squad."
Following their promotion, Fulham spent around £100m on players including midfielder Jean Michael Seri, striker Aleksandar Mitrovic and defender Alfie Mawson during the summer transfer window.
But they have won just three of their 22 league games this season and have one win in their last 10 matches in all competitions.