A local primary school was also placed on lockdown while police dealt with the incident, but the restrictions have since been lifted.
Avon and Somerset Police were called to the Royal United Hospital around 9.45am on Friday, to a report an unknown man had telephoned making "verbal threats".
A second call making more verbal threats was received at about 10.15am.
Police had already been at the hospital when the first call was reported, and they liaised with site security. More officers were dispatched to the scene when the second call came through.
A man was then reportedly seen carrying "an item, which there were concerns could have been a bladed weapon", in the vicinity of the hospital at around 10.35am.
Avon and Somerset Police said the report has not yet been confirmed.
"Enquiries are ongoing to identify the man in question to establish what they were in possession of," said a spokesperson.
The Royal United Hospital was placed under lockdown "as a precaution", and police also advised a local primary school to lock down.
Both measures have since been lifted.
"We’d like to reassure the public that there have been no reported injuries and a police presence remains in the area," said a police spokesperson at 1pm on Friday.