The pastor of one of America's biggest churches has stepped down from leadership amid accusations of an extra-marital affair.

Bob Coy was Senior Pastor at Calvary Chapel Fort Lauderdale in Florida for almost 30 years, which has approximately 20,000 members and 1,000 staff.

A statement released by the church on Sunday reads: "On April 3, 2014, Bob Coy resigned as Senior Pastor ... effective immediately, after confessing to a moral failing in his life which disqualifies him from continuing his leadership role at the church he has led since its founding in 1985."

Though the church has not confirmed exactly what the "moral failing" is, many speculate that Coy has been unfaithful to his wife of over 30 years, Diane, with whom he has two children.

Calvary Chapel is the 14th largest church in the US, with assets of an estimated $135 million. Its congregation was stunned by the announcement of Coy's departure during a packed meeting on Sunday evening, where a letter of apology from the former pastor was read out.

"Most people were shocked," church member Robert Milne told Sun Sentinel. "A lot of people were hurt; a lot of people are disappointed."

"Of course I forgive him," Milne hastened to add, noting that Coy had spoken extensively on human weaknesses in the past. "We're all sinners and we've all slipped here and there."

The official statement released on Calvary Chapel's website says that having stepped down from his position, Coy will now be "focussing his full attention on his personal relationship with God and with his family".

It continues: "The governing board of the church is providing counsellors and ministers who will help guide him through the process of full repentance, cleansing and restoration."

"Trusting in God's providence, protection, provision and direction, the staff of Calvary Chapel Fort Lauderdale will continue our mission to 'make disciples,' through regular services at all campuses and through a myriad of other ministries the church has established over the years.

"A team of assistant pastors already on staff will maintain their usual rotating schedule as teaching pastors for all services."

Coy's personal Twitter account makes no mention of these recent events. His last tweet, sent on April 4, simply reads: "In His name the nations will put their hope – Matthew 12:21."