Explaining that he was unable to come to Atlanta on such short notice, Mr. Lee then received two letters from the organization’s lawyer, Dexter M. Wimbish, threatening him with suspension or removal as president of the Los Angeles chapter if he did not come soon to explain himself.

Mr. Wimbish did not return calls to his office, nor did the Rev. Raleigh Trammell, chairman of the organization’s national board. A woman who identified herself as Renee Richardson left a voice-mail message for a reporter, saying the organization did not “discuss internal matters.” She did not return follow-up calls.

The issue attracted the attention of the president of the Los Angeles City Council, Eric Garcetti, who wrote to the board in support of Mr. Lee.

Because chapters of the leadership conference operate autonomously and presidents are picked by local boards, it is not clear that the national organization has the authority to remove Mr. Lee from his post, which he has held for two years.

“It’s been our position that the local board hired him,” said Reginald Byron Jones-Sawyer, chairman of the local board and secretary of the California Democratic Party. “And, in fact, we are also the ones that approved his stance on the position of marriage equality. We have asked the national board if we have violated any procedures, and we have not gotten an answer.”

Mr. Lee, the former pastor of In His Steps, an African-American Wesleyan church in Los Angeles that he described as “very conservative,” said he saw failures both in the leadership of the conference (“Dr. King would be turning over in his grave right now,” he said) and the largely white anti-Proposition 8 movement that did not more actively seek the support of church-going African-Americans.

“The black church played a significant role in Proposition 8 passing,” Mr. Lee said. “The failure of the campaign was to presume that African-Americans would see this as a civil rights issue.”