A special motion put forward by the First and Deputy First Ministers to unequivocally condemn the rioting, campaign of intimidation and attacks on elected representatives received cross-party support on Monday morning.
Pressure is mounting on Stormont to find a solution to the ongoing protests.
Mr McGuinness said: "There can be no excuses for street violence that has left 28 police officers injured, Belfast City Council staff injured, drivers of cars and buses intimidated and threatened."
He said the damage done to Northern Ireland's reputation worldwide would be difficult to repair, "but repair it we must."
There can be no ifs or buts - it must be condemned plain and simple.
First Minister Peter Robinson told the Assembly that a debate on the flags issue will still have to come.
The DUP leader said that he shared the frustration and anger that many people had about the removal of the Union Jack.
Mr Robinson said that he defended the right to protest, before adding: "The right to protest is as fundamental to the democratic process as the right to vote."
"But let's be clear, there is no right to attack police officers or council staff. There is no right to destroy property. There is no right to threaten or to intimidate.
"There is no right to endanger life, harm, injure or kill.
"There is no right to attack elected representatives because you don't agree with their views."
Alliance Party leader David Ford expressed his sympathy to all victims of threats and violence.
Alliance MP Naomi Long, Sinn Féin MLA Gerry Kelly and Councillor Jim McVeigh have all received death threats. A number of Alliance representatives had their offices or homes attacked, while DUP councillor Sammy Brush had his home vandalised at the weekend.
"All of these incidents are an affront to democracy," said Mr Ford, adding his party had borne the brunt of the attacks.
Frustration and anger should not flow out into violence - it must be channelled into democratic processes.
UUP leader Mike Nesbitt also condemned the violence.
"Anyone who attacks a police officer; anyone who attacks an elected politician; anyone who attacks any individual or engages in illegal activity on our streets fails to understand the values that are encapsulated in the Union flag," he said.
"In doing what they did, the rioters lost the very argument they want to advance."
SDLP leader Alasdair McDonnell said politicians also needed to condemn "the anti-democratic mindset that says Belfast City Council had no right to take the decision that it did."
Meanwhile TUV leader Jim Allister asked whether culture was "Sinn Féin's new theatre of war".
"The unionist community is expected to sit back and consent benignly to the trampling underfoot of its culture and identity by forces that are insatiable and still live by the mantra of "Brits out". That is what the taking-down of the flag crystallises in its own particular way," he said.
"I abhor and condemn all the violence of the hangers-on and the threats, arson and intimidation.There is no justification for any of it, and it should stop. It should never have started."
Police said a number of protests passed without incident at the weekend.
Up to 300 people gathered on the Peace Bridge in Londonderry on Sunday afternoon while later that day around 30 people demonstrated at the bottom of the Shankill Road in Belfast.
A PSNI spokesperson said: "Police have carried out evidence gathering in relation to the actions of some of these protesters and a file will be prepared for the Public Prosecutions Service."
Meanwhile, nearly 2,000 people attended a demonstration outside Belfast City Hall on Saturday.
A senior police officer warned loyalist paramilitaries had orchestrated some of the violence that marred the city at the end of last week and appealed for calm.
The Northern Ireland Human Rights Commission has also condemned the trouble.