Bournemouth, Christchurch and Poole council said it had no choice but to declare a major incident and condemned the "irresponsible" behaviour of crowds who gridlocked roads, dumped rubbish, parked illegally and some who reportedly got involved in fights.
Extra police patrols have been brought in and security is in place to protect refuse crews who the council said faced "widespread abuse and intimidation" as they emptied overflowing bins.
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Thirty-three tonnes of waste was cleaned up along the full stretch of coastline on Thursday morning, in addition to eight tonnes collected between the piers on Wednesday, the council said.
It issued 558 parking enforcement fines, a record number, and said extra parking enforcement is now in place.
Council Leader Vikki Slade said: "We are absolutely appalled at the scenes witnessed on our beaches, particularly at Bournemouth and Sandbanks, in the last 24-48 hours.
"The irresponsible behaviour and actions of so many people is just shocking and our services are stretched to the absolute hilt trying to keep everyone safe. We have had no choice now but to declare a major incident and initiate an emergency response."
The council said there had been "a number of incidents reported which involved excessive alcohol and fights".
Roads, which were gridlocked into the early hours, according to the council, now have signs telling people the area is full.
Ms Slade said the popular tourist destination is not yet in a position to deal with the numbers of visitors it has had this week, nor to handle the fallout from such large crowds.
She said: "Please do not come. We are not able to welcome you yet."
Assistant Chief Constable Sam de Reya, of Dorset Police, said: "These are unprecedented times and we are urging people to stay away from the area of Bournemouth Beach and other Dorset beaches.
"The declaration of a major incident allows us to bring agencies together so we can take actions available to us to safeguard the public as much as possible."
She urged people to take personal responsibility and "think twice" before coming to the area.
She said: "Clearly we are still in a public health crisis and such a significant volume of people heading to one area places a further strain on emergency services resources.
"This influx of visitors to our area places a significant increase in demand on our service and we would ask people to please bear with us.
"We would therefore stress again that we are asking people to please stay away from the area."
Bournemouth East MP Tobias Ellwood added his voice to the calls for people not to go to the area.
He tweeted: "With 1/2 million visitors in Dorset, roads are gridlocked, hindering emergency vehicles & beaches are full - with Dispersal Orders on both piers. I've asked Police Minister to dispatch additional police if Dorset requests."