It comes after UDA leader Jackie McDonald held talks with the DUP and UUP in the wake of Belfast City Council's decision to reduce the number of days the Union flag flies at City Hall.
The forum will be chaired by First Minister Peter Robinson and UUP leader Mike Nesbitt.
Invitations are to be extended to other unionist parties, representatives and interested groups.
A statement said: "The forum will be a body through which unionists could meet to consider matters of interest and concern to the unionist community.
"The forum will not be a decision-making body but would act as a body within which a consensus might be built and implementation of any actions left to individual organisations.
The agenda that we have drawn up for the first meeting is the agenda of people who have indicated that these are the issues that need to be addressed, these are the issues that we want to talk about
"It would seek to engage positively with representatives from all sectors of the Northern Ireland community."
Forty-one police officers have been injured during disturbances linked to the flag decision, while several politicians have received death threats and businesses have been affected.
A number of peaceful protests took place across Belfast on Tuesday night.
Small groups of loyalist and nationalist youths gathered close to the bottom of the Albertbridge and Mountpottinger Roads.
There was a heavy police presence but roads in the area remained open to traffic.
It stood in contrast to Monday night's violence which resulted in eleven police officers being injured and fifteen arrests.
The first meeting of the Unionist Forum will be held "soon" at Stormont.
Some of the issues which are to be discussed include flags, parades, and increasing the voter turnout in unionist areas.
Mr Robinson said he hopes people will engage with the process and move beyond protests.
"What we are saying to people is that a protest is a mechanism for people to be heard and once they are heard and they have made their point then we want to provide them beyond the protest with a vehicle that can start getting changes to fulfil the unionist cause," he said.
"More and more I hear from the people as they are interviewed that flags isn't the only issue, that there are other issues that they want to talk about."
Mr Nesbitt outlined what he hopes to achieve with the forum.
"What we have offered is to first of all to acknowledge the frustration that has boiled over into anger for which go beyond the flag to issues with culture and heritage, economy and politics," he explained.
The aim in bringing everyone together is you see where everyone is and how far apart they are and if you can achieve a consensus then you can reach out to the rest of the community with a single voice
"Secondly it's to show leadership in saying you are actually destroying the argument you are promoting by some of the street protest in particular the violence, and thirdly to go beyond condemning in a better way which is a strategic brains rather than brawn way forward."
Neither of them would be drawn on who exactly will attend the forum but it is expected to include members of the Progressive Unionist Party, the Loyal Orders and community leaders.
Working groups may be established to go out to the wider community.
Meanwhile deputy First Minister Martin McGuinness said unionist leaders must take action to prevent further protests.
The Sinn Féin MP said: "I am looking forward to meeting with the other party leaders on Thursday, when we can discuss the current issues affecting us all.
"We need to move forward on all these issues jointly and on the basis of equality.
"I also call on unionist leaders to recognise that they need to do more to bring to an end these UVF organised protests and violence."
Alliance leader David Ford said parties should be working "on a cross community basis and not on a cross unionist basis".
He said: "The only solution to deliver a shared future must come from a consensus from all groups and not from parties working in different tribal blocks.
"We will not achieve anything if the unionist parties put forward their demands on behalf of one section of the community and thus turning the debate into one in which issues are won or lost for different sections.
"What we need to do is to reach agreement on these issues for all sections and not just one grouping."
SDLP Leader Dr Alasdair McDonnell welcomed the forum and encouraged any conversation that could end the protests.
He said: "If a wider conversation within unionism will bring an end to the illegal and violent street protests, the murder attempts and attacks on police officers, the attacks on property, the multiple death threats issued to elected representatives across the political spectrum and the massive disruption to traders and citizens, the SDLP will not stand in its way.
"However, this is not the sum total of leadership. The people of Northern Ireland are looking to the First Minister and Deputy First Minister to jointly demonstrate that they can lead a government not purely defined by tribal lines but one which shows leadership when it comes to reconciliation, positive expressions of identity and dealing with the past."