Vanarama National League side Hartlepool have confirmed allegations of abuse have been made following Saturday's clash with Ebbsfleet at Victoria Park.
The north-east club were fined £7,500 – including £5,000 suspended for 18 months – after being found guilty of failing to ensure their fans refrained from using racially-abusive language in a home game against Dover in September.
Saturday's statement read: "Following today's fixture against Ebbsfleet United, we can confirm that allegations of two incidents during the game have been made.
"It is important to state that, at this stage, these alleged incidents are unsubstantiated and will be subject to a full investigation.
"We will hide nothing in our thorough examination of the facts and will respond to any enquiries from any authorities.
"As importantly, once we have carried out a full investigation we will identify any action required and, regardless of this, will not be distracted from our commitment and efforts to promote diversity and educate inclusivity.
"Hartlepool United condemn abuse of any nature and we will continue to work closely with the relevant bodies to ensure that Victoria Park is a safe and welcoming environment for all supporters, staff and players."
Pools boss Dave Challinor, who was shown a red card after the final whistle for what he described as "a coming together" with an Ebbsfleet player, said he "heard nothing", as did opposition manager Kevin Watson.
Challinor said: "We lost and there has been allegations. I've heard nothing and things will be dealt with out of my control. That's where we are at.
"I can't control those things, it's bigger than I am. I'm in charge of managing my dressing room."
Fleet manager Watson said: "I didn't hear anything at all and we are miles away from where the allegations were made: one from our goalkeeper behind the goal, one from the far side involving Jermaine McGlashan. I've not heard anything so can't comment.
"It's been reported, both by myself and Dave with the officials. They followed the protocol to call us over, then a tannoy announcement and then see the referee afterwards.
"I don't think you report something like that unless it happened.
"I've spoken to both players. (Goalkeeper) Jordan (Holmes) immediately ran over as it came from behind the goal. He can't see or identify anyone with his back to the crowd."
McGlashan later tweeted: "Class from the few Hartlepool players that came to see how I was today after being racially abused not for the first time in a game, no room whatsoever for it & hope it gets dealt with accordingly! @kickitout."
Challinor, his staff and Hartlepool's fans were frustrated by what they felt were time-wasting tactics from struggling Ebbsfleet, who boosted their survival hopes with a 1-0 win.
The game ended with players from both sides squaring up and one home supporter encroaching onto the pitch.