The Ireland Palestine Solidarity Campaign said it feels vulnerable following a decision by Bank of Ireland to close its bank accounts in the Republic and in Northern Ireland.
The bank has declined to comment on the move. It follows similar decisions in other European countries including Austria, Germany, France and the UK where banks have closed down accounts of Palestinian campaign groups.
The Ireland Palestine Solidarity Group has had accounts with Bank of Ireland since it was first established in 2001.
It said it was first contacted about this issue by the bank in July with a series of questions including what the funds in the account were used for and if it transferred any money to Palestine and if so to whom.
The Campaign's treasurer Martin O'Quigley said it fully answered the bank's questions and provided it with a copy of its constitution and of its audited accounts for 2015.
It said most of its funds are spend in Ireland raising awareness of Palestinian issues.
The only money or aid it sends to Palestine is to a factory in the West Bank which manufactures traditional Palestinian scarves which the campaign buys as solidarity items.
But it said Bank of Ireland informed it that it does not fit the bank's appetite for risk as Palestine is deemed to be a high-risk country.
The Campaign asked the bank for an extension to keep the accounts operational until December so it could make new arrangements and have enough time to ensure that all donors who were funding the group through standing orders had been given the details of new bank accounts.
It had been difficult to contact people in August because many were on holiday, it said.
But the bank refused the request and closed the accounts on 27 September.
The Ireland Palestine Solidarity Group has opened new accounts with AIB but said it feels vulnerable that a bank could withdraw facilities without what it believes to be any good reason.
It is considering an appeal to the Banking Ombudsman.
Sinn Féin deputy leader Mary Lou McDonald branded the decision by Bank of Ireland as "outrageous".
"The Ireland Palestine Solidarity Campaign are an established advocacy group that have spent years protesting against the treatment of the Palestinian people.
"To close their account citing that they associate with a 'high risk country'...this is not only outrageous; this is insulting to the Palestinian people.
"Bank of Ireland cannot stay silent on this matter," she added.