The Rev. Marcus Cosby, pastor at Wheeler Avenue Baptist Church, told Houston television station KTRK and the Houston Chronicle that safety concerns had prompted Wright's decision.
Cosby told the Chronicle that Wright cited three reasons for canceling: "the safety of the institution to which he has been invited; the safety of his family, which has been placed in harm's way; and for his own safety."
Wright also canceled his appearance Tuesday in Florida at a Tampa-area church. The hosting church said it asked Wright to cancel his scheduled three-day appearance because of security questions.
Wright had been expected to be in North Texas over the weekend to be honored by the Brite Divinity School in Fort Worth, but it was unclear whether he would still be attending.
"His schedule is pending," Joan Harrell, minister of communications for Trinity United Church of Christ in Chicago, where Wright was pastor for nearly four decades, told The Dallas Morning News for its Tuesday online editions. The newspaper said that she wouldn't elaborate.
Harrell didn't immediately return a phone call from The Associated Press on Wednesday.
Videos of remarks Wright has made have been circulating widely on the Internet and news programs. Wright's sermons to his predominantly black congregation have included him shouting "God damn America" for its treatment of minorities. He has said the U.S. government invented AIDS to destroy "people of color" and has also suggested that U.S. policies in the Middle East and elsewhere were partly responsible for the 2001 terrorist attacks on New York and Washington.
"I think we have taken Dr. Wright out of context with sound bites," Cosby said. "After all these years, I am not going to kick him to the curb over sound bites."
In a speech last week, Obama sharply condemned Wright's remarks and the preacher's refusal to acknowledge progress in race relations. But the Illinois senator refused to repudiate Wright.
In North Texas over the weekend, Wright is supposed to speak at a Saturday luncheon at Paul Quinn College in Oak Cliff and be honored that night at Friendship-West Baptist Church in the Red Bird area.
Frederick Haynes III, pastor of Friendship-West Baptist, said Tuesday night that the Dallas events are "all systems go," but he acknowledged that security issues could keep Wright away.
"We're going to honor him," he said. "The question is, basically, regarding his presence."