It has been become the latest group to oppose a scheduled visit by the 66-year-old to a Christian event he is staging in Blackpool later this month.
The Council, which represents more than 500 mosques and Islamic organisations, told The Guardian: "In the past, the government has banned individuals whom they claim are 'not conducive to the public good'.
"Mr Graham's remarks are on record and clearly demonstrate a hatred for Muslims and other minorities.
"We would expect the government to apply its criteria here. If it does not, it will send a clear message that it is not consistent in challenging all forms of bigotry."
The oldest son of late preacher Rev Billy Graham is due to speak at the Festival of Hope at the Winter Gardens conference centre.
Is it being organised by the Billy Graham Evangelistic Association (BGEA) in partnership with local churches. Franklin Graham currently serves as presidents of the BGEA.
Speaking during an exclusive interview with Premier earlier this year, Mr Graham said: "I'm not coming to preach hate.
"I'm here to preach about a saviour - Jesus Christ who can make a difference in our lives if we put our faith and trust in him."
The Association has previously described the Festival of Hope as a "positive and encouraging event".
But 8,400 people signed a petition started by a local pastor Nina Parker which said Franklin Graham should be denied access to the UK.
Three MPs from the north-west of England have also expressed concern. Labour politician Gordon Marsden said previous comments made by Franklin Graham were "incompatible with what Jesus said in the Bible".
Among the criticisms made of Franklin Graham, he is purported to have said during an interview shortly after the 9/11 attacks on the US in 2001 that Islam is a "very evil and wicked religion".
Home Office guidance tells border staff: "If it is conducive to the public good not to admit a person to the UK because of their character, conduct or associations you must consider refusing entry or leave to remain."
The Billy Graham Evangelistic Association told Premier: "The Billy Graham Evangelistic Association is bringing the Lancashire Festival of Hope with Franklin Graham after being invited by local churches, and is working in partnership with them to hold this event in September—as it has done in hundreds of countries and cities around the world for more than 60 years.
"The ministry is excited about the support in the Lancashire area from more than 150 churches of various denominations that are eager for this opportunity to bring the life-saving, hope-filled message of Jesus Christ to thousands of people there.
"The Festival of Hope will be a positive and encouraging event.
"There will be music, and Franklin Graham will share with people the same kind of message his father, Billy Graham, preached during his historic events in England, which is the joy that comes through having Jesus Christ in your life as Lord and Savior.
"If anyone is concerned about what they may have heard regarding this event, the Billy Graham Evangelistic Association invites them to come and see it for themselves.
"The Festival of Hope with Franklin Graham will be held September 21st, 22nd and 23rd at the Winter Gardens in Blackpool.
"The event is free and everyone is invited."
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