An American pastor imprisoned in Turkey because of his Christian faith has had his appeal denied and remains jailed on charges of "membership in an armed terrorist organisation", campaigners say.

According to the American Centre for Law and Justice (ACLJ), Pastor Andrew Brunson appealed against his imprisonment but Turkish authorities denied his request.

Brunson, 48, led a Protestant church in Izmir and was jailed on December 9 after being detained in October.

His family say he was arrested on false terrorism charges after he was accused of links to US-based cleric Fetulah Gulen, whom Turkey blames for the failed coup in July.

Together with his wife Norine, originally from North Carolina, Brunson has lived in Turkey for 23 years.

The ACLJ, which is representing the pastor, says no evidence has been provided by the Turkish authorities to justify Brunson's detainment.

"The charging documents do not present any evidence against him," the Centre said in a statement.

It accused officials in Turkey of denying Brunson attorney-client privilege and said he was previously denied access to a Bible, though he has now been allowed a copy of the New Testament.

"Although Pastor Andrew has finally been allowed a family visit and some access to his attorney, he is still wrongfully imprisoned and the charge he faces is serious," the ACLJ said.

"Pastor Andrew must be released. We are continuing our diplomatic efforts to engage the incoming US administration, and moving forward with an appeal of his case."

On Saturday, evangelist Franklin Graham urged Christians around the world to pray for Brunson and his wife.

In a Facebook post, Graham said: "He spent Christmas in prison. Andrew Brunson is an American citizen who has been serving as a pastor in Turkey for more than 23 years. He and his wife raised their family there.

"Over two months ago, he was unexpectedly detained and has been unfairly charged with being a member of an armed terrorist organisation and is still imprisoned. These are very serious charges. I spoke with Pastor Andrew's wife yesterday, prayed with her, and assured her that I would share this with you. You can understand her concern.

"I ask that you join me in praying specifically for Pastor Andrew's protection and release. Please share your encouragement and prayers with Mrs Brunson in the comments below and I will be sure she knows. I hope you will also share this post with others who will pray.

"The Bible says, 'Continue to remember those in prison as if you were together with them in prison, and those who are mistreated as if you yourselves were suffering' (Hebrews 13:3)."

Brunson's family said in an earlier statement: "Andrew's strong faith has always been at the centre of his life and that has never been more evident than his pastorship in Turkey.

"His love and concern for the people of Turkey is unmistakable, as he has dedicated 23 years of his life serving them."