Mr Ford said his colleagues will "continue to work for a fair, shared and equal society for everybody" after Belfast Councillor Laura McNamee was advised by police not to return home on Tuesday due to a security risk.

Reacting, Mr Ford said: "Any threat to a democratically elected politician for carrying out their duty, for saying what they said they would do is utterly outrageous."

On Wednesday the First and deputy First Ministers also condemned the threats.

"They need to stop and those people in positions of influence need to use their influence to ensure that these activities cease," Martin McGuinness said.

Peter Robinson added: "There are some issues that parties are not going to agree on, and that's a fact anywhere in the world and in those circumstances those issues have to be determined democratically, and peacefully, it has to be said. I certainly deplore any personal attack or threat on any elected representative or indeed any person in Northern Ireland."

On Wednesday a second protest was organised outside the Alliance constituency office in east Belfast, with Union flags and red, white and blue balloons.

Local Alliance MLA Chris Lyttle said the party's constituency services continued despite attempts to "disrupt" work.

"The participants in these protests must be aware that they are causing serious damage to local businesses working flat out to deliver much needed economic development and jobs in this area and I would urge them to cease this disruption and I would welcome them to direct their concerns in a more safe and constructive manner," he said.

There are serious and significant sensitivities about flag flying, but these decisions must be taken on the basis of sound, reasoned discussions and democratic vote, not as a result of mobs seeking to beat down the door of City Hall.

Secretary of State Theresa Villiers

Violence flared in the city centre on Monday night following the passing of the Alliance motion to display the Union flag at City Hall on 17 designated days.

The plan, which follows the accepted protocol on flying the Union flag at Stormont, was backed by 29 votes to 21. Nationalists had previously wanted to remove it altogether.

Mr Ford described the vote as a "balanced decision in line with the Equality Commission recommendation that the Union flag should only fly on designated days".

"Alliance proposed a compromise that nationalists accepted, which unionists will not yet recognise as a valid compromise."

He said his party had not backed Sinn Féin and the SDLP but had suggested an alternative proposal. He said a similar motion was passed in Lisburn City Council seven years ago.

DUP Lagan Valley MP Jeffrey Donaldson said unionists had been "very clear" in condemning the violence and intimidation.

"This country is still part of the United Kingdom and the Union flag is the flag of this country. It's recognised in international law so why can't we fly the flag on our premier civic building in our capital city?" He also asked.

In the House of Commons on Wednesday, Secretary of State Theresa Villiers also condemned the violence scenes.

She said the decision on flying the Union flag was "a matter for Belfast City Council to decide".

Ms Villiers said: "I fully appreciate the strength of feeling on the flying of flags, but there is nothing that could possibly justify the scenes of disorder that were witnessed outside City Hall in Belfast earlier this week."