The Northern Ireland Assembly will be recalled later this week to discuss violent scenes after an anti-immigration protest in Belfast.
Several businesses were attacked during the violence on Saturday and business owners said the Islamic community was deliberately targeted.
Four men appeared in court on Monday to face charges linked to the violence.
The Police Service of Northern Ireland (PSNI) said on Monday evening it was aware of social media posts calling for protests across Northern Ireland in the week ahead.
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The PSNI said officers would monitor the situation and would be engaging with groups likely to be affected by any protests.
Late on Monday police said they were dealing with ongoing disorder in the Donegall Road area, and urged people to avoid the Donegall Road and Sandy Row areas.
First Minister Michelle O’Neill and Deputy First Minister Emma Little-Pengelly said there was “no justification for racism or for the violence and intimidation that occurred on our streets on Saturday”.
A special meeting of Belfast City Council also took place on Monday evening.
Ms Little-Pengelly said she spoke to Northern Ireland Secretary Hilary Benn on Monday.
“We agreed on the importance of strong, collective opposition to all violence and disorder,” she posted on the X, formerly Twitter.
“I also highlighted importance to recognise that there are many with genuinely held concerns not involved in violence or racism.”
Earlier, Stormont Speaker Edwin Poots said the Assembly would be recalled at noon on Thursday after a recall petition submitted by the Alliance Party and backed by the SDLP and Sinn Féin.
MLAs will discuss a motion condemning “criminal damage and targeting of businesses in recent days”.
The motion also calls on Ms O’Neill and Ms Little-Pengelly to finalise the draft Refugee Integration Strategy and associated Thematic Delivery Plan and present it to the Executive, and to bring forward the renewed Race Relations Order, and set out the process of replacing the Racial Equality Strategy 2015/25 by the end of 2024.
In a joint statement, the two leaders said they had spoken earlier with PSNI Chief Constable Jon Boutcher.
“While people are entitled to take part in peaceful protest there is no justification for racism or for the violence and intimidation that occurred on our streets on Saturday,” they said.
“Today we have spoken to the chief constable and offered him our full support and we pledged to work to deliver a shared, peaceful and inclusive society.
“There must be a zero-tolerance approach to racism and wanton destruction. Nobody should have to live in fear or threat of violence.
“Again, we would appeal to anyone with information to contact the PSNI.”
Stormont’s justice minister, Naomi Long, said the scenes had been hugely damaging, describing some people as scared to leave their homes because of the colour of their skin.
Police mounted a significant security operation during a lengthy confrontation between anti-Islamic protesters and those taking part in an anti-racist rally at Belfast City Hall during which fireworks and other missiles were thrown.
The force said it then prevented an attempt by protesters to march to Belfast Islamic Centre, but that sporadic violence broke out in other parts of the city.
Three police officers were injured in the disorder and the PSNI said those involved will be dealt with “using the full force of the law”.
Speaking to the media on Monday, Ms Long said she was “absolutely distraught” about what happened.
“These scenes have been broadcast around the globe of the rioting right across the UK and in our main city,” she said.
“It’s hugely damaging to our reputation but it’s also incredibly damaging to our community.
“We have people in Belfast today who are afraid to go outside of their homes because of the colour of their skin, or because of their religion, or because of their perceived background, because they’re afraid that they will be attacked on the streets.
“This kind of xenophobia and racism and bigotry isn’t acceptable. It is intolerable, and from my perspective when it tips over into violence it is a very serious issue, both for the department of justice and for the police service.”
Ms Long warned anyone considering travelling to Northern Ireland to riot: “If you do, you will be held accountable in front of the courts. You will be pursued. There isn’t a free pass to come to Northern Ireland and engage in this kind of behaviour.
“We need as a community in Northern Ireland to stand against this. We need the political leadership. We need leadership from the PSNI. We need leadership from within our community to say that they do not want this visited on the streets of Belfast.
“We have experienced violence over the years. We know the damage it can do. We above all should understand the vulnerability of people who are being subjected to this kind of intimidation and it’s up to all of us to play our part in saying this is not welcome in Northern Ireland.
“If you engage in it, whether you are from Northern Ireland or from outside Northern Ireland, you will be held accountable.”
Earlier, Ms Long told the BBC’s Good Morning Ulster programme: “We are already seeing now on social media people making preparations for another round of this this week.
“This cannot continue, we cannot have this kind of Islamophobia, xenophobia and hatred on our streets.
“People have a right to an opinion when it comes to immigration, but it needs to be an informed opinion. What we are seeing instead is radicalisation of people online through disinformation and outright lies. It is incredibly dangerous.
“If there are lessons to be learned around the policing operation I have no doubt whatsoever they will be learned.”
Policing Board chairman Mukesh Sharma described the violence in Belfast as “deeply depressing and disturbing”.
“As a board, we join in the condemnation of all those who engaged in this disorder, and we welcome police commitments to bring all those responsible to justice,” he said.
“There is no place for hate in our community.
“We all have a real job of work to do to provide reassurance to the community that the violent actions of a few are not representative of our society.
“I welcome the increased police engagement at this time with affected and concerned communities, and also trust that all those officers injured in the course of the disorder make a speedy recovery.”
Retail NI chief executive Glyn Roberts said: “These attacks are despicable and should be condemned. Racism has no place in our community and those behind these attacks should be brought to justice.
“Our thoughts are with the owners and staff of these businesses going through such a traumatic experience.
“We hope that the police will learn lessons from last weekend and ensure that these disgraceful, racially motivated attacks on business owners are prevented in future.”