Police guidelines were followed by three constables involved in a drowning accident, senior officers have said.
Divers recovered a man's body from the River Exe on the Quay at St Leonards in Exeter, Devon on Tuesday.
Two men who tried to save the man claimed the police response was too slow and have made a complaint.
The matter has been referred to the Independent Police Complaints Commission but senior officers say procedures were followed.
Many people on Exeter's waterfront witnessed the incident, which happened at about 1345 BST.
"We risked our own lives doing it and they should've done the same"
Eyewitnesses said after an apparent disagreement with police constables, the man plunged into the river, disappearing under the water when he was about halfway across.
The river is about 50m (164ft) wide at the quay with a varying depth of up to 15m (50ft) and a strong undertow in places.
There are signs along the quayside warning people about the dangers of swimming in the river.
Ryan Curwen and Greg Clifford dived in to save him but gave up after about 20 minutes.
Mr Curwen described the police response as "terrible" and "slow".
"The first police officer to get in the water had to get a boat instead of getting wet. He got in a little canoe and paddled out in it."
Mr Clifford told the BBC he believed the officers should have gone into the river immediately.
"They should have jumped in after him, like we did," he said.
"We didn't have to, but we risked our own lives doing it and they should've done the same."
The two men went to Heavitree Road Police Station on Wednesday morning to make a complaint.
A lifebelt on the quayside was not used.
'Splashing around'
But senior officers insisted the three constables had followed correct police procedures and guidelines.
National police guidelines advise officers not to enter the water if they cannot see the person who is in trouble in case they put themselves in danger.
The officers' action has also been defended by the Police Federation.
Federation spokesman Steve Tovagliari said: "My understanding is the gentleman jumped into the river of his own accord and initially was just splashing around.
"Once he got out into the middle of the river, the officers realised he was in danger and immediately set in place an appropriate plan of action."
The man's body was eventually recovered by divers about four hours later, at about 1745 BST.
The force said all its officers were trained in life saving and had helped to save 30 people from potentially life-threatening incidents last year.
It also worked with the RNLI to train officers and had a team of specially-trained divers to help with underwater searches.
A spokesman said the force worked closely with the other emergency services who were fully equipped and trained to deal with water-related incidents.
"We would advise all members of the public not to enter the water if they have been drinking," he added.
The incident has similarities to an accident in Wigan last May, in which 10-year-old Jordon Lyon drowned in a pond while trying to save his younger sister.
Two Police Community Support Officers (PCSOs) were criticised for not attempting to rescue the boy.
But Assistant Chief Constable Dave Thompson of Greater Manchester Police said they acted correctly as neither police officers nor PCSOs were encouraged to carry out this type of underwater rescue which was "fraught with danger".
The IPCC said it was considering how the investigation into the River Exe incident would be dealt with.
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