Cunningham dismissed Fury and said he had no interest in talking.
"There's a code that runs through the streets," Cunningham said. "The guys who talk a lot are chumps."
The 24-year-old Fury (20-0, 14 knockouts) will be making his U.S. debut, and all but one of his 20 professional fights have been in the United Kingdom or Ireland. The 12-round fight will begin in the afternoon so it can be aired to a prime-time audience in the UK.
Under IBF rules, the winner will face Bulgaria's Kubrat Pulev. The winner of that fight will become the No. 1 contender for IBF and WBO heavyweight champion Wladimir Klitschko.
"I'm a man on a mission, and I mean business," Fury said. "Steve's got a lot to be thankful for - he's been a world cruiserweight champion; he has a lovely wife and lovely children - but I'm going to retire you, Steve."
Fury easily defeated American Kevin Johnson last December, and his signature win was a 2011 unanimous decision over previously unbeaten Dereck Chisora to win the British and Commonwealth heavyweight titles.
In Cunningham's last fight, the 36-year-old (25-5, 12 KOs) lost a controversial split decision to Tomasz Adamek. It was Cunningham's second fight since moving up from cruiserweight, a division in which he won two world titles.
He will give up six inches in height to the 6-foot-9 Fury, and Cunningham expects his opponent to attempt to lean on him throughout. Fury also weighs nearly 50 pounds more than the 203-pound Cunningham.
Cunningham's cruiserweight background makes him a swift heavyweight, and he could attack Fury from a distance.
"A lot of guys don't want to get up in the ring with a straight-up giant," Cunningham said. "He's a literal giant. But I'm a fighter. That's what I do. I grew up in Philly."
North Philadelphia lightweight Karl Dargan (12-0, 6 KOs) will fight on the undercard against a yet-to-be-named opponent. Dargan, 27, scored a split decision on Feb. 23 against Ramesis Gil.
Contact Matt Breen at firstname.lastname@example.org and @matt_breen on Twitter.