Officers were left injured in clashes with protesters outside a mosque in Southport on Tuesday after three girls were killed in a knife attack.
Home Secretary Yvette Cooper said police should be shown respect while they investigate the Southport attack as she condemned the "thuggery" of rioters.
Alice Dasilva Aguiar, nine, Bebe King, six, and Elsie Dot Stancombe, seven, were all fatally stabbed in Southport, Merseyside, on Monday.
Eight other children suffered stab wounds and five are in a critical condition, alongside two adults who were also critically injured, police said.
Hundreds of people took part in a vigil on Tuesday evening outside Southport’s Atkinson arts venue, with many in tears as they laid flowers and cards of remembrance.
But some protesters on Tuesday separately gathered outside a mosque in the town where missiles were thrown at police and cars were set alight.
Merseyside Police said on X: "A number of officers have been injured, cars set alight and a shop broken into and looted in Southport this evening. This is completely unacceptable.
“We're gathering evidence and those responsible will be brought to justice.”
Officers earlier said they believed some of those involved in the disorder were “believed to be supporters of the English Defence League”.
The unnamed 17-year-old suspect in the case is from Wales, police have said, but false claims had spread online that he was an asylum seeker who had arrived in the UK by boat.
Speaking to broadcasters on Tuesday night, Ms Cooper branded the incident "a total disgrace".
She said the community had thanked the police for their "heroism", adding: "That is why it is so appalling to now see those same police facing violent attacks from thugs on the streets who have no respect for a grieving community.
"It is a total disgrace. Frankly, this is a time when everyone should be showing respect for a community and for the police."
She went on: "Frankly the scenes of thuggery that we have seen on the streets of Southport this evening bear no relation to the way in which the Southport community has been coming together to support each other and to support grieving families."
In the Commons she had earlier urged social media companies to "take some responsibility" for speculation in the aftermath of the attack, as the case was "about children and their families who will be grieving".
Police said a name shared on social media in connection with the suspect is "incorrect", adding: "We would urge people not to speculate on details of the incident while the investigation is ongoing."
Assistant Chief Constable Alex Goss said: “It is sickening to see this happening within a community that has been devastated by the tragic loss of three young lives.
“In the last 24 hours, we have seen overwhelming support and sympathy from the community and wider Merseyside communities for the families who are currently trying to deal with their loss and care for victims injured during the major incident.
“Yesterday, our officers and other members of the emergency services were faced with one of the most difficult situations they will ever face. Tonight, they find themselves being attacked as they endeavour to prevent disorder.
“The actions in Southport tonight will involve many people who do not live in the Merseyside area or care about the people of Merseyside.
“There has been much speculation and hypothesis around the status of a 17-year-old male who is currently in police custody and some individuals are using this to bring violence and disorder to our streets.
“We have already said that the person arrested was born in the UK and speculation helps nobody at this time.
“Our officers should not have to face this, but we will be there tonight to ensure the safety of the local community who have suffered enough, and will arrest those involved in criminal behaviour.”
