The Kirk said it gave reassurances to immigration officials about the two would-be visitors but their visas were refused because "they could not prove they were wealthy enough to be allowed into the UK".
Church officials said they are concerned by the move, which they argue could jeopardise major international events in future.
The Home Office said it does not comment on individual cases.
The pair had hoped to visit Glasgow this year as part of moves to create a twinning link between the Kirk's Glasgow Presbytery and the Diocese of Hyderabad.
But their efforts to come to the country have been repeatedly frustrated, the Church claims.
An official dealing with the case wrote to acknowledge that the Church would bear the costs of the visit, the Kirk said.
But the refusal document added: "I am not satisfied the bank statement is an accurate reflection of your financial circumstances. Given the above, I am not satisfied you are genuinely seeking entry as a general visitor for a limited period as stated by you not exceeding six months."
The presbytery's joint clerk, Rev Graham Blount, said he remains committed to building the link with Hyderabad.
He said: "We are deeply concerned at the refusal of the UK Government to grant visas to two of our invited partners. Despite the Church of Scotland guaranteeing their travel arrangements as well as their accommodation and subsistence while they are here, the refusal seems grounded in their personal financial circumstances."
Presbytery members now plan to write to the UK Government and local MPs to voice their concerns.
Rev Blount added that the visa refusal "threatens to frustrate" other major international events, such as the World Council of Churches General Assembly, for which a bid is currently being considered.
A Home Office spokesman said: "We do not routinely comment on individual cases."
