Last month, when asked if he intended to mount a White House bid, Mr. Perry told a reporter for The Des Moines Register that he was “getting more and more comfortable every day that this is what I’ve been called to do. This is what America needs.” But to reporters in Austin, Mr. Perry denied there was a purely religious connotation to his remark, saying: “There’s a lot of different ways to be called. My mother may call me for dinner.”

To many political observers and to his critics, it sounded like backpedaling. “You saw the politician and not the man of faith,” Mr. Henson said.

Mr. Perry announced in June that he was inviting governors and people from across the country to join him in a day of prayer and fasting at Reliant Stadium because, as his official proclamation put it, “As Jesus prayed publicly for the benefit of others in John 11:41-42, so should we express our faith in this way.” Although he has invited people of all faiths, Mr. Perry has described it as a “Christian-centered” event to pray for the troubles of the nation. The rally is being organized and financed by the American Family Association, an evangelical organization listed as an antigay hate group by the nonprofit Southern Poverty Law Center.

Opposition to the governor’s involvement in the event — and his support of the American Family Association — has been widespread, including several leaders of the Methodist community in Texas, the governor’s own denomination. They said in interviews that the Methodist tradition teaches inclusion and that for the governor to sponsor an event that they viewed as exclusionary to Jews, Muslims and those of other faiths was wrong.

“I don’t think there’s any question that it’s divisive,” said Tom Spencer, a Methodist and chief executive of Interfaith Action of Central Texas, a multifaith group once led by Mr. Perry’s former pastor. “I think the political motivations behind it are transparent.”

The Rev. Kevin Young, pastor of Linden United Methodist Church, a 400-member church in Cass County, a Republican stronghold in East Texas, was one of more than 50 religious leaders who signed a statement drafted by the Anti-Defamation League objecting to the governor’s participation in the rally. “I’m not happy that our governor is using an event like this essentially to appeal to a voting bloc,” Mr. Young said. “I just don’t see that it’s a sincere effort to seek divine guidance for the state.”