The appeal came as a Sudanese man appeared in court charged with attempted murder and as UK Prime Minister Keir Starmer and politicians in Northern Ireland condemned the violence by "masked thugs" that had targeted ethnic minorities.
Hundreds of protesters, many with their faces covered, had attacked police and burned vehicles in a number of locations across Northern Ireland late on Tuesday after a video of the knife attack went viral.
"We want to make it absolutely clear that overnight unrest is not welcome, and peaceful protest is the only way forward," the family of the victim, Stephen Ogilvie, said in a statement.
"We have many migrants who make a deeply valuable contribution to our country ... We do not want this terrible tragedy to be used to divide people or fuel hostility," it said.
Speaking in parliament, Starmer said the attack raised serious questions but that "driving people out of their homes is not ... the right way to respond," adding that all those involved in violence would face "the full force of the law".
The suspect in the attack in north Belfast, a 30-year-old Sudanese man named as Hadi Alodid, appeared in court where he was remanded in custody.
Alodid was charged with the attempted murder of Ogilvie, with threats to kill a radiographer and with possession of a knife.
Alodid, who appeared in court via video link, made no reply to the charges when they were put to him through an Arabic interpreter.
The court heard Alodid said "I've killed someone, I don't know if they are dead" while in hospital receiving treatment for a hand injury and told medical staff "I will kill you".
Ogilvie, who is in his 40s, suffered significant injuries to his face and back, the court heard.
He remains in a serious condition in hospital in Belfast and is understood to be in an induced coma.
Videos of the attack had circulated online all day on Tuesday, sparking calls on social media for violent protest.
Police had to help one family escape from a burning house.
Several cars and a bus were set on fire and reduced to shells.
Local resident Jamie Corry, 33, said he could only watch on as his house went up in flames.
"I was actually standing right there watching my whole house just go up, slowly but surely," he told Reuters.
"I told them and all, when they were lighting a car up on fire, that's my property, that's my property ... and they still didn't care."
Northern Ireland's First Minister Michelle O'Neill described the violence perpetrated by the masked men as "nothing less than disgusting cowardice".
The attack, which is currently not being treated as terrorism, comes at a time of heightened tensions in the United Kingdom following the murder of a student who was handcuffed by police as he lay dying from stab wounds after his killer, a Sikh man, falsely alleged a racist attack.
It also follows repeated protests about immigration, with populist parties saying the UK's asylum policy had allowed dangerous men into the country.
Amid online calls for more protests on Wednesday, Northern Ireland's police chief said an extra 200 officers were being deployed on the streets.
"These idiots didn't just target ethnic minority groups ... they targeted society," Chief Constable Jon Boutcher said.
Alodid entered Northern Ireland across the Irish border in February 2023, having flown to Dublin from Paris.
He claimed asylum upon arrival and in September 2023 was granted leave to remain in the UK until 2028.
Democratic Unionist Party leader Gavin Robinson said the "open porous border" with Ireland should be closed following the "medieval" knife attack.
But Northern Ireland Secretary Hilary Benn said there was "strong co-operation between the UK authorities and the Irish authorities in seeking to deal with illegal migration across the Common Travel Area, but the answer is not to say the Common Travel Area is the problem".
with PA
