Billy Graham's grandson, Tullian Tchividjian, has resigned as the pastor of a Florida megachurch after admitting an adulterous relationship.

Tchividjian, 43, the son of Graham's eldest daughter Virginia, became pastor of the Coral Ridge Presbyterian Church in 2009, in succession to its founding pastor D James Kennedy. He sought to move the church away from the "culture wars" with which it was associated.

In a statement he said that he had discovered his wife Kim was having an affair and that he had requested a sabbatical to "focus exclusively on my marriage and family". However, the affair continued and they had separated. He said: "Sadly and embarrassingly, I subsequently sought comfort in a friend and developed an inappropriate relationship myself."

He admitted the affair after being approached by church leaders.

Tchividjian's statement continued: "Both my wife and I are heartbroken over our actions and we ask you to pray for us and our family that God would give us the grace we need to weather this heart wrenching storm. We are amazingly grateful for the team of men and women who are committed to walking this difficult path with us.

"Please pray for the healing of deep wounds and we kindly ask that you respect our privacy."

He tweeted yesterday, "Welcome to the valley of the shadow of death...thank God grace reigns here."

The executive pastor of Coral Ridge, Rob Pacienza, told the Washington Post: "Several days ago, Pastor Tullian admitted to moral failure, acknowledging his actions disqualify him from continuing to serve as senior pastor or preach from the pulpit, and resigned – effective immediately. We are saddened by this news, but are working with and assisting Pastor Tullian and his family to help them through this difficult time, and asking people to join us in praying that God will bring restoration through this process and healing to all involved."

Tchividjian's time at Coral Ridge has been far from plain sailing. The church had experienced years of decline after the death of its founder and Tchividjian's relative youth and fresh approach was seen as an advantage. He eschewed the right-wing politics to which the church was accustomed – Kennedy was a founder member of Jerry Falwell's Moral Majority movement – and instead emphasised grace and forgiveness.

Shortly after his appointment, a group led by Kennedy's daughter Jennifer called for his dismissal, but the church voted to keep him and the group left to form a new church.

In a 2011 Leadership Journal interview, he said: "It was tremendously uncomfortable coming to worship every Sunday morning during that time not knowing who liked you and who hated you. He said that among other tactics used by those who opposed his ministry: "They put petitions on car windows during the worship service. They started an anonymous blog, which was very painful. Here we were trying to build consensus and there's this anonymous blog fueling rumors and lies. The blog almost ruined my wife's life. Anonymous letters were sent out to the entire congregation with accusations and character assassinations. It was absolutely terrible."

A church statement said that no successor had been named: "While we do not yet know whom God will direct to lead our congregation in the near future, we trust the Lord's guidance during this transition period, knowing He is our hope."