The family of Mr Lawrence yesterday lodged a formal complaint against the police officers who went to the murder scene, and are considering civil action against white youths suspected of his stabbing.
"I don't think anyone could fail to have the deepest sympathy with the family of Stephen Lawrence," Mr Howard said.
"What happened on that day was an absolutely terrible trag-edy and we all grieve for the parents. I understand how des- perate they must feel," he told Channel Four News.
Mr Howard said the family's complaint against the police would be "considered by the entirely independent Police Complaints Authority".
"I would like to consider whether a public inquiry would add anything of significance to that investigation, which will, of course, be very thorough," he said.
The jury at an inquest into Mr Lawrence's death, held at Southwark coroner's court in south London, yesterday decided that the teenager, a pro-mising A-level student, had been unlawfully killed.
Family members maintain that the police failed to carry out a thorough search based on an anonymous tip-off they received and did not use the criminal intelligence available to track down the suspects before vital evidence was lost.
Outside the court, a prepared statement by the teenager's mother, Doreen Lawrence, 44, was read out.
"There were times this week when I was not sure whether I was in a court room listening to evidence of how my son was killed or at a circus watching a performance. It became a mockery of trying to get to the truth," she said.
"What was coming across for me was that none of the officers saw fit to go round to known suspects' homes even to eliminate them from the inquiry.
"The wall of silence was not only in the surrounding area where my son was killed but with the police officers who were supposed to be investigating the crime.
"Right from the start on the night our son was murdered, it seemed that in the minds of the police he was only a black boy, so why bother. No one can convince me otherwise."
Mrs Lawrence added: "There are two questions I would like the police to answer: Are all the officers trained in basic first aid, or was it because they just did not want to get their hands dirty with a black man's blood?"
The Metropolitan Police's Assistant Commissioner Ian Johnston, said last night it was a matter of deep personal regret that his officers have not been able to see Mr Lawrence's murderers successfully prosecuted.
"I am deeply sorry that Mrs Lawrence feels as she does about the police. I would like to say again that I believe we did all we could," he said.
The family's solicitor, Imran Khan, appealed for witnesses to come forward to help assist an action for damages which the family is planning to bring against white youths suspected of his murder.
"We are strongly considering taking further legal action against those individuals we think may have been responsible," said Mr Khan.
Mrs Lawrence broke down in tears on hearing the verdict of unlawful killing, after the jury agreed that her son had died from an unprovoked attack by five white youths.
On directing the jury, the Southwark coroner, Sir Montague Levine, said it would be perverse to give any other verdict. "This was an horrific crime and totally unprovoked in which a group of cowardly young men attacked an unsuspecting youth, which resulted in him bleeding to death," he said.
He urged society to increase its efforts to rid itself of the paranoia of racism and its intolerance, adding: "We must teach our young, both in families and in our schools, that each individual regardless of their race, regardless of their colour, regardless of their religion, has the right to live peacefully without fear of intimidation."
The court was also told how Mr Lawrence died from severe haemorrhaging after being stabbed in the chest and in the arm. Five white youths were accused of murdering him as he waited for a bus in Eltham, south-east London, in April 1993, but the charges were dropped by the Crown Prosecution Service. A subsequent private prosecution brought by Mrs Lawrence failed.Reuse content