Jennifer Korn, who as a deputy director of the public liaison office manages contact between the White House and faith groups, sends out invitations to policy briefings and the “listening sessions.”

Ms. Korn invites senior West Wing advisers such as Jared Kushner, Ivanka Trump and Kellyanne Conway to visit the groups, which range from 20 to 100 guests and are often tied to specific faith-related legislation, executive orders and court appointments. Ms. Trump recently sat in on a meeting with female faith leaders that Mr. Moore and Mr. Jeffress attended.

“We are the front door to the White House,” Ms. Korn said, echoing Mr. Moore’s words.

Mr. Jeffress, another core member from the campaign board, has been one of Mr. Trump’s most reliable evangelical advocates, regularly appearing with him in Trump Tower in New York and then in the White House.

“I can’t look into the president’s heart to know if he really personally believes these positions he’s advocating, or whether he thinks it’s smart politics to embrace them because of the strong evangelical influence in the country,” Mr. Jeffress said in an interview. “But frankly, I don’t care. As a Christian, I’m seeing these policies embraced and enacted, and he’s doing that.”

Mr. Jeffress, who once said President Barack Obama’s politics could lead to the rise of the Antichrist, said the issues that evangelicals discuss at the White House “go beyond what most assume,” including opioid abuse and criminal justice overhaul. He and Mr. Moore are sympathetic to the Deferred Action for Childhood Arrivals program, known as DACA, that shields young undocumented immigrants, which is often viewed as a progressive cause.

When he is in the Oval Office with faith leaders, Mr. Moore said, they try to “personalize” issues for Mr. Trump, including in a recent discussion on DACA, when the group told the president that he should view the issue as a father and grandfather.