DUP Enterprise Minister Arlene Foster has called for an end to street protests over the Union flag.
The Fermanagh MLA said she was very concerned about the damaging impact on local traders.
She made her remarks as it was revealed on Thursday that an SDLP MLA and a DUP councillor had received death threats.
It brings to eight the number of politicians who have received death threats in the past ten days.
Violence has followed some protests over last week’s decision to limit the number of days the union flag is flown at Belfast City Hall.
Mrs Foster said the timing of that debate had been “wrong headed”.
She made an appeal directly to the protestors on BBC Radio Ulster’s Evening Extra programme on Thursday, saying: “Take it off the streets and let’s make it into a process where we can all move forward together in a unified way.
“This party has always been talking about coming together and unifying and moving the union forward because we believe in the union, it’s good for everybody in Northern Ireland.
“So let’s make that a reality.”
In a statement, SDLP enterprise trade and investment spokesperson Patsy McGlone has said Mrs Foster’s call for flag protests to stop for the sake of the local economy “is long overdue”.
The mid-Ulster MLA said: “The minister has known for days the impact that these protests are having on the local economy, but she and her party have hidden behind partisan politicking against the democratic decision of Belfast City Council.
“If she is so determined to make Northern Ireland a successful region, why has she let traders down by keeping silent for so long?”
In the past week, violence has flared in parts of Northern Ireland in the wake of the street protests.
At least 29 police officers have been injured and over 40 people arrested. Six youths, aged 13-14 have been charged, bailed and subjected to night time curfew over the trouble.
Alliance Party members and premises have been targeted by loyalists since last Monday’s vote on the city hall flag.
Two senior DUP members – Jeffrey Donaldson and Edwin Poots – have also been warned of death threats, which they believe are from dissident republicans and linked to their stance on the flags issue.
Alliance, Sinn Fein and SDLP councillors voted to limit the flying of the flag while the Democratic Unionist Party (DUP) and Ulster Unionists (UUP) opposed the move.
Two Belfast politicians are the latest to receive death threats amid ongoing protests over flags.
The SDLP’s Conal McDevitt, MLA, and the DUP councillor, Guy Spence, received the threats on Thursday.
Mr McDevitt got the threat in the post and the threat to Mr Spence was made in a telephone call to Belfast City Hall.
Over the past few days, death threats have been issued against members of the Alliance party, Sinn Fein and the DUP.
In a separate incident, the DUP said its constituency office in Richhill, County Armagh, has been vandalised.
The office is used by the Newry and Armagh MLA William Irwin.
The windows of the building have been smashed and paint has been daubed on the walls.
There have been a series of attacks on the homes, cars and offices of public representatives since the beginning of the flag dispute on 3 December.
It followed a decision by Belfast City Council to restrict the flying of the union flag at Belfast City Hall from 365 days a year to designated days only.
Since then, death threats have issued against the DUP leader and First Minister, Peter Robinson, his party colleagues Edwin Poots and Jeffrey Donaldson, Sinn Fein’s Gerry Kelly and Jim McVeigh and the Alliance MP Naomi Long.
There has also been an attempt to murder a policewoman who was guarding Ms Long’s constituency office in east Belfast on Monday evening.
Police said 15 masked men armed with iron bars smashed the car windows before lobbing a petrol bomb inside.
She cheated death in the attack and detectives have launched a murder bid probe.