The SDLP, which was one of the parties that voted to limit flying the flag at Belfast City Hall, has tonight said one of its Assembly members had also received a death threat.
South Belfast MLA Conall McDevitt said the warning was posted to him.
"The police are investigating a specific threat against me," said the representative, who has been outspoken on the flag issue.
"This will not deter me from representing the people of South Belfast and working for an inclusive, peaceful and prosperous society."
SDLP leader Alasdair McDonnell said: "This is a cowardly, cynical act by those determined to drag our society back into the shadows of the past, but they should be aware that we will not be intimidated and they will not prevail.
"The whole of the SDLP stands in solidarity with Conall."
In Co Armagh, the office of DUP Assembly member William Irwin in Richhill has been attacked, with windows smashed and paint daubed on the property.
"Whilst this incident does not compare to some of the other disgraceful attacks and threats on elected representatives, it is an attack on the democratic process nonetheless," said Mr Irwin.
"Attacking democratic facilities and services is mindless and completely pointless when such facilities are in place to serve our communities' needs."
Meanwhile, Guy Spence - Northern Ireland's youngest councillor - has also received a death threat.
A telephone call was made to Belfast City Hall this afternoon and was transferred to the 20-year-old Democratic Unionist who represents a ward in the north of the city.
A DUP spokesman said: "He is obviously concerned but he won't be put off his council work. Guy Spence has work to do and he will just get on with it."
Mr Spence was among a number of elected representatives whose cars were vandalised when loyalist protesters tried to storm Belfast City Hall after the controversial decision to restrict flying the Union flag was taken on December 3.