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Sims said her "thoughts are with all those injured in tonight's horrific incident, their family and friends, and all of those affected by the terrible tragedy" and thanked all the emergency services and members of the public "who came to the assistance of the injured".
Sims said it had been "a joyous day" in the city "with hundreds of thousands of people lining the streets to celebrate Liverpool Football Club's victory parade".
"Sadly, at 6pm this evening as the parade was drawing to a close, we received reports that a car had been in a collision with a number of pedestrians on Water Street in Liverpool City Centre.
"A number of people have been injured and were taken to hospital.
In addition, a large number of people of all ages were treated at the scene that did not require hospital treatment."
She urged people to refrain from sharing "distressing footage" from the incident online, but called for videos to be passed to the police.
Sims said a "robust" traffic management plan had been in place for the parade.
"In the lead-up to this event we had been working closely with event organisers and a robust traffic management plan was put in place for the parade, which included a number of road closures throughout the route and the city centre," she said.
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A police spokesperson said: "We would ask people not to share distressing content online but to send the footage or information directly to us @MerPolCC or pass on information by calling 101 quoting log 784.
"Information can also be passed on anonymously via Crimestoppers on 0800 555 111."
What we know so far...Shortly after 6pm, police respond to an incident in Liverpool city centre after a car collided with several pedestrians.
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In a post on social media, Everton FC said: "Our thoughts are with all those who have been affected by this serious incident in our city."
Manchester United also posted on social media, saying: "Our thoughts are with Liverpool FC and the city of Liverpool after today's awful incident."
A Premier League statement said: "Everyone at the Premier League is shocked by the appalling events in Liverpool this evening, and our heartfelt thoughts go out to all those injured and affected.
"We have been in contact with Liverpool FC and have offered our full support following this serious incident."
PM Starmer: The whole country stands with Liverpool
The prime minister, Sir Keir Starmer, has said he has spoken to Liverpool City Region mayor Steve Rotheram "about the terrible events" on Monday evening.
He said: "Tonight, I have spoken to Steve Rotheram about the terrible events in Liverpool and the remarkable bravery shown by the police and other emergency services.
"They are supporting and caring for those injured in these terrible events.
"Everyone, especially children, should be able to celebrate their heroes without this horror.
"The city has a long and proud history of coming together through difficult times.
"Liverpool stands together and the whole country stands with Liverpool."
Rotheram said in a statement: "Our hearts go out to all of those affected, especially those who have been injured.
The police are investigating and I'm being kept updated on developments."
Liverpool Riverside MP Kim Johnson, whose seat includes the city centre, said: "I sincerely hope all those involved are safe and get home to their loved ones soon."
'We saw a car run over people'
Liverpool FC held an open-top bus parade to celebrate its Premier League title win, with fans lining the streets along the 10-mile route.
Councillor John Hughes estimated in excess of one million people were attending, beating the 750,000 present for the 2019 Champions League parade.
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