Published Tuesday, 04 December 2012
It is understood the councillor was singled out on Twitter over the issue.
News of the threat comes after a loyalist protest was held at the Alliance Party's offices in east Belfast on Tuesday afternoon.
Up to 100 people turned up outside and fixed Union flags and red, white and blue balloons to the front of the building, before later dispersing.
Alliance MLA Chris Lyttle insisted his party won't be intimidated.
"Some Unionist representatives and their staff have gone as far as to encourage the protest at Alliance Party constituency offices, despite the serious violence that followed the original protests at City Hall on Monday night," he said.
"This demonstrates a complete disregard for the safety of people, businesses, and the PSNI in east Belfast."
Mr Lyttle added: "People can seek to intimidate my party colleagues and I from doing our job, but we will continue to work on the democratic mandate we have been given to deliver a shared and better future for all in east Belfast."
The latest protest comes after rioting in the city centre, sparked by the passing of a controversial motion to restrict the flying of the flag at Belfast City Hall.
Nationalists wanted to remove it altogether, but the Alliance Party - which holds the balance of power - proposed an amendment to display it on 17 designated days.
Their plan, which follows the accepted protocol on flying the Union flag at Stormont, was backed by 29 votes to 21.
But the decision led to riots involving up to 1,500 loyalists, which resulted in three arrests and 18 people being injured overnight.
Alliance councillors have suggested they would be in favour of a Union flag flying at the cenotaph in City Hall as a compromise.
The DUP are to put forward a proposal in the New Year.
Meanwhile, north Belfast Sinn Féin MLA Gerry Kelly has said that he has received a death threat in the aftermath of Monday night's rioting.
"The threat obviously follows in the aftermath of last night's attack on democracy at the Belfast City Hall by loyalists," he said.
"The people who made the threat should understand that neither I nor any of the other Sinn Féin representatives will be deflected from pursuing equality in the city of Belfast or anywhere else."
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