Marvin Rees expressed his support for the Jubilee year, an ordinance God prescribed for the Israelites arriving in the Promise land. It included the cancellation of debts and freeing of slaves after 50 years.
The evangelical Christian said: "When you look at things like the Year of Jubilee, the Biblical mandate is not to have an economic system which compounds inequalities through spirals of wealth and spirals of poverty."
According to Leviticus, the Jubilee year also required that slaves and prisoners be freed and property be returned to its original owners.
Mr Rees, who works elected Mayor of Bristol in May 2016, questioned resistance by some conservative Christians to the state tackling inequality through taxation. He said Christians should be campaigning for a fairer society.
He said: "Particularly, when you think about the right-wing church in the United States, they don't like state intervention in taxes.
"I say the year of Jubilee was a massive tax and if it was good enough for Jesus to quote it in Luke 4, that it's enough for us to think about how we apply it today."
Mr Rees expressed concern that the wealth gap between the rich and poor in the UK is growing and appealed to churches to be bring about change.
He said: "One day we'll stand before God and say, 'why did all these things happen?'.
"God may say, 'Listen, I gave you a brain and a fantastic social organisation that many people would envy - in terms of the Church - I gave you a democracy. Did you use all those things in the way that you could have?'"