The IFC Ethical Finance Round Table, which has attracted senior representatives from government, financial services, academia and the voluntary sector, aims to "bring together Islamic and ethical banking as the bedrock to a systemically stable and prudent banking sector".
Islamic finance seeks to avoid the payment of interest on loans, preferring partnership, profit and risk sharing, and it also shuns certain types of investment.
Graham Burnside, chairman at Tods Murray, said: "We believe that it is time for the government to formalise their involvement to position Scotland as a global ethical finance hub."
It would bring together key players in the market to put the conditions in place for "developing and testing new financial models of banking".
The round table says recent polls show more than half of Scots want to see some of their money invested using green or ethical criteria - higher than the UK average, showing that "the need for a more ethical form of banking and finance is paramount against the backdrop of the ongoing financial crisis".