Glentoran Football Club says it is saddened that BNP members handed out pamphlets at the Oval before their home game with Glenavon on Saturday.
Supporters of the party were seen carrying placards and handing out pamphlets as part of a protest campaign against the war in Afghanistan. The east Belfast club said it did not welcome "these types of groups" outside the Oval.
"Glentoran Football Club has a strong tradition of being an inclusive football club that appeals to a broad range of supporters and players from across all communities in Northern Ireland", the club said in a statement.
"Our strong cross community ethos does not align itself with any political party and we are saddened that such an incident has happened. We do not welcome these types of groups outside of our football club as we continue to provide an inclusive and welcoming atmosphere at the Oval for local football supporters."
DUP East Belfast MLA Robin Newton said he received calls from members of the public complaining about the presence of BNP members outside the football ground last weekend. Mr Newton described their presence at the match as "uninvited and unwelcome".
"A number of constituents have contacted me to express their disgust at the presence of the BNP outside their local club," he said. "They go to the Oval to support the Glens and enjoy a game of football; they don't want to be faced with BNP messages of hate. I presume this BNP presence is some sort of campaign to raise their nauseous profile, and I appeal for everyone to stand as one to reject their message.
"The BNP should pack up their messages of hate and disappear. They have been rejected time and time again, they represent no-one, and we don't want them in our midst."
Alliance councillor Mervyn Jones says the group "has no place" at the sports ground.
"I am disgusted that the BNP would try to take advantage of a football match to try and canvass support for their sickening views," Mr Jones said. "I am glad that Glentoran fans have given this group the red card as this type of activity has no place anywhere near our sports grounds. As a Glentoran supporter, I strongly resent any attempt to link Glentoran Football Club to the BNP.
"Inside the ground I spoke to a number of people and everyone I spoke to was opposed the presence of the BNP, which might be considered the only positive thing to come from this disgusting episode."
In a statement, the BNP said it was seeking "an end to the illegal and immoral war in Afghanistan."
The party said it took to "the streets of Belfast in a peaceful and democratic manner to collect signatures for a petition to be handed in to the government calling for the immediate withdrawal of all British troops from that conflict."
"For the DUP, and Robin Newton in particular, to attack the BNP for this pro-peace message is an example of the most extreme hypocrisy yet seen in Northern Ireland", the statement added.