The Home Secretary said last night that a new offence of racial harassment and racially-motivated violence was to be created by the Crime and Disorder Bill this autumn.
He told a Commons meeting of the Black Jewish Forum: "The measures in the Crime and Disorder Bill will send out a strong message that racial violence and racial harassment have no place in our society and will not be tolerated."
Under proposals being drafted by the Home Office, it is expected that the new offence would increase the maximum sentence for actual bodily harm from five to seven years, if an attack was racially motivated.
For offences of racially- motivated grievous bodily harm, which already carries a maximum life sentence, judges would be expected to add an extra two years to the sentence they would otherwise have imposed.
Enhanced punishment would also be proposed for all other offences, such as arson, where racial motives were proved.
The move follows Home Office confirmation that Mr Straw would next week announce a wide-ranging investigation, headed by a senior judge, into the Stephen Lawrence killing.
Mr Straw last month met Stephen's parents, Doreen and Neville Lawrence, who have been campaigning for a public inquiry. It is expected the new inquiry will cover the handling of the case by the police and prosecuting authorities as well as the wider implications of the killing, which took place at a bus sop in Eltham, south-east London, in 1993.
The Crown Prosecution Service dropped charges against two white youths; a private prosecution by the family collapsed after the evidence of a key witness was ruled inadmissible; and earlier this year an inquest jury returned a verdict of unlawful killing by five white youths in an unprovoked racist attack.
The Stephen Lawrence Family Campaign said the inquiry decision vindicated the view "that the police and prosecuting authorities completely mishandled this case".
But Simon de Banya, the campaign's spokesman, said the inquiry might have to be delayed as the family was considering the possibility of a second private prosecution which would have to be held first. The family's lawyers are expected to meet early next week to consider their next move.
After the inquest ruling, the Daily Mail identified five men as the killers of Stephen Lawrence and David Winnick, Labour MP for Walsall North, yesterday questioned their decision not to rise to the challenge to sue the newspaper for libel. "Like most people, if I was named in a newspaper as having committed a very serious crime like murder, I know what I'd do to protect my reputation," he said.Reuse content