Hospital managers said on Wednesday they were experiencing "significant" patient admissions and were at "full-capacity protocol".
They apologised to patients and urged people to attend only in emergency.
The Irish Nurses and Midwives Organisation (INMO) said staff were seriously concerned.
"Nurses are fearful that patients are being put at risk on a daily basis while they strive to deliver basic care," said the union.
"There are wards in the hospital with insufficient nurses to deliver basic nursing care. This situation is now causing untold human suffering for patients."
The hospital's escalation policy has been partially invoked over the past six weeks to deal with increasing bed demand.
The policy is usually only used in exceptional circumstances.
The INMO called on the Irish Health Service Executive (HSE) to:
The INMO's industrial relations officer, Maura Hickey, said: "The problem cannot be solved by placing extra beds on in-patient wards.
"This is a tried, flawed and failed practice of the past which should never be revisited."
The BBC has contacted the HSE for comment.
An Irish nurses union has expressed concern at what it called a "crisis situation" at Letterkenny University Hospital due to bed capacity.