The Ulster People's Forum announced on Wednesday that they will also hold localised protests outside council offices to coincide with monthly meetings.
There have been 181 arrests and 128 charges in connection with the disorder, which followed a Belfast City Council vote in early December changing the Union flag policy at City Hall.
"If people wish to continue to protest at City Hall that's their right to do that as long as they don't engage in acts of violence," spokesperson Jamie Bryson told UTV Live Tonight - referring to the weekly Saturday demonstrations which have been held in the city centre.
The change in strategy comes after an Ulster People's Forum meeting, attended by community representatives, was held in Belfast last weekend.
Although the organisation said they do not speak for everyone, Mr Bryson told UTV Live Tonight that they will support anybody who continues to protest in other ways as long as "it's non-violent and non-threatening".
"What we heard from the people on the ground is that they are looking for leadership, what we're trying to do is show leadership - trying to show a way forward," Mr Bryson said.
What we don't want is young people getting criminal records - we don't want anybody getting criminal records so that's why we're advocating at this time white line protests.
"We have to be clear - anybody who continues to protest in other ways as long as it's non-violent and non-threatening we will also continue to support that," he added.
He said that he had "no problem" with acts of civil disobedience as long as they were non-threatening and not intimidating.
Last week a senior police officer vowed to step up the operation against those blocking roads across Northern Ireland, revealing he had drafted in Metropolitan Police who dealt with the 2011 London riots.
The Police Federation says the ongoing dispute, sporadic street violence and the severe dissident threat means the PSNI is facing the "most challenging period" of its history.
Chairman Terry Spence told UTV Live Tonight earlier this week that "normal policing" has been suffering as a result of the physical and financial strain.
"It's apparent that because of the very severe threat from dissident republicans, coupled with the very serious public disorder which is being orchestrated by loyalist paramilitaries that the police service are being distracted from delivering normal policing in Northern Ireland," he said.
Mr Bryson said that his organisation had been "clear from the start" they condemned violence and intimidation.
The Ulster People's Forum say they are currently engaging in a process to find a strategy to move things forward.
"We also want to get the broader support of the Protestant/Unionist/Loyalist community which I think we do have - but we want to maintain that and that's the thinking behind this."
Behind the scenes intense negotiations are taking place on a daily basis to try and defuse what's been a highly volatile situation on our streets.
UTV’s Sharon O’Neill
DUP MLA for Lagan Valley Edwin Poots has welcomed the announcement.
"Any society welcomes the right to protest because that's the sign of a free society but do it within the law," he said.
"People will still make their voices heard. Ultimately they can make their voice heard at the polling booth because that's where they can really make the difference."
However Conall McDevitt, SDLP MLA for South Belfast, has described the strategy as "deeply counter-productive."
"This whole episode has been one monumental disaster for loyalism.
"And I think the time is well past for them to call off their protests and if they are serious about engaging in politics, to bring their arguments into committee rooms and to try and find an agreed way forward."
The NI policing board member added: "Loyalism needs to face up to the fact that this has been one unmitigated disaster for their community and their leaders have been found wanting - wanting in terms of their ability to understand how to do politics properly and wanting in terms of their ability to understand how dangerous and damaging street protest and street violence is."
Earlier this week Sinn Féin deputy First Minister Martin McGuinness revealed he had met with flag protesters.
South Belfast MLA Alex Maskey told UTV protesters "need to have dialogue with the rest of us".
"Let's get to a point where the protests come off the streets and people are allowed to go about their business and have a dialogue about how we respect each other - Britishness and Irishness," the Sinn Féin representative said.
A major marketing initiative for Belfast city centre has been launched after the ongoing dispute hit trade.
Backin' Belfast is aimed at encouraging shoppers to return to city centre to enjoy its pubs, restaurants and stores.