Falwell, who was already on an indefinite leave of absence, did not return a call from the AP seeking comment.
The uncertainty developed a day after Falwell issued a statement to The Washington Examiner publicly disclosing that his wife had an extramarital affair and saying the man involved had been threatening to reveal the relationship "to deliberately embarrass my wife, family, and Liberty University unless we agreed to pay him substantial monies".
Falwell said he was seeking mental health counselling after dealing with fallout from the affair, which he said he had no role in.
"Over the course of the last few months this person's behaviour has reached a level that we have decided the only way to stop this predatory behavior is to go public," the statement said.
But hours before the school official confirmed Falwell's resignation, Reuters reported that he knew of his wife's affair and participated in some of the liaisons as a voyeur. The news agency based the information on an interview with Giancarlo Granda, whom they identified as the man involved in the affair.
Falwell, an early and ardent supporter of President Donald Trump, began a leave of absence from the university on August 7 after an uproar sparked by a photo he posted on social media showing him with his pants unzipped, stomach exposed and arm high around the waist of his wife's pregnant assistant. Falwell has said the photo was taken at a costume party during a family vacation.
Critics of the photo said it was evidence of hypocritical behaviour from the leader of a university where students must follow a strict code of conduct that includes modest dress and a ban on alcohol consumption and premarital sex.
The possible break with Falwell came amid growing calls for an overhaul of leadership at the school, where alumni recently launched a campaign urging him to step aside.
"I really think the board of directors should have done this a long time ago, and if there's anybody who needs to go next, it needs to be them," said Maina Mwaura, a Liberty graduate who helped organise a June letter from Black alumni criticising Falwell.
"This school has become the laughingstock of the country," Mwaura added, noting that the board could have prevented the current furore had it acted more quickly to rein in Falwell. The founder's son was given a long leash for poor behavior, Mwaura said, "because he was the rainmaker" who brought in significant financial resources.
Falwell's work to shore up Liberty's finances after taking over as president in 2007 bolstered his already significant goodwill among the school's board members, several of whom were close to his late father. But as the younger Falwell's propensity toward divisive public behavior grew — and particularly after his endorsement of Trump in early 2016 — dissatisfaction built up with what some critics saw as a shift toward being conservative first and Christian second.
- AP