The Financial Services Union has described a meeting with Northern Ireland's finance minister Conor Murphy as a "very constructive and a good starting point" to discuss the future of banking in Northern Ireland.
The FSU raised the issue of NatWest's strategic review of Ulster Bank's operations in the Republic of Ireland, as well as news that Bank of Ireland is to review its operations in the North, and said the lack of detail around both was "unacceptable" to staff and customers.
"We encourage the minister to use his influence to request both banks to publish the terms of reference without delay," the FSU's general secretary John O'Connell said.
According to the FSU, over 600 staff based in the offices of Ulster Bank in Donegal Square East and Danesfort in Belfast are directly working on supporting Ulster Bank in the Republic of Ireland.
"If Ulster Bank were to close in the Republic these jobs would be at risk," Mr O'Connell said.
The FSU also asked Mr Murphy to establish a banking forum in Northern Ireland, consisting of key stakeholders including unions, employers and the government.
It said Mr Murphy had shown "genuine engagement" on the issues it raised.