Sgt Nigel Clement, a member of the Metropolitan Police Territorial Support Group, told the inquiry that he arrived in a van with other officers when Stephen was lying on the pavement, and quickly carried out a search of the area to look for suspects. But Stephen Kamlish, representing the Lawrence family at the inquiry into the 18-year-old's murder, said they did not accept that Sgt Clement arrived when he said he did.
Sgt Clement insisted he was telling the truth about the events of the night in April 1993 when Stephen was killed in Eltham, south-east London.
Sir William Macpherson, chairman of the inquiry, adjourned proceedings because he said he was concerned that Sgt Clement was being accused of lying without being warned beforehand. According to inquiry rules, a witness must be informed of any allegation made against them before they give evidence.
"I had no idea there was a question that they [Sgt Clement and other police officers] would not only be accused of being inefficient but also be accused of telling lies and inventing things," Sir William said.
Evidence from Sgt Clement and from Inspector Steven Groves, who arrived on the scene at the same time, was postponed until they have taken legal advice.
Before Sgt Clement left the witness box, he told the inquiry that when he arrived on the scene he did not see any blood from Stephen's injuries. "I did not see any blood. I did not get close enough to see if he was breathing because the pavement was very dark," he said.
He also said he did not recall seeing anyone at the scene except two other police officers. But Mr Kamlish told him if he had been at the scene at that time he would have seen Duwayne Brooks, Stephen's friend, as well as Conor Taaffe and his wife Louise.
The inquiry heard evidence from people who had witnessed events on the night.
Helen Aviary, who was 13 at the time, said she had not seen any police officers administering first aid to Stephen. "I felt quite shocked that the police that were there were not really doing anything," she said. Her sister, Catherine, who also witnessed the events, said she had seen a police officer crouching down by Stephen, apparently trying to find a pulse, but not obviously administering first aid.
Three men - Neil Acourt, 22, Gary Dobson, 22, and Luke Knight, 20 - were cleared of Stephen's murder at the Old Bailey in 1996. The case of two others - Jamie Acourt and David Norris, both 21 - never came to full trial.
The Lawrence family have alleged that police errors following Stephen's murder were the result of racism.
The hearing continues on Monday.