Speaking at the Board of Deputies of British Jews' annual gala dinner in London, Mr Straw also outlined the government's actions and proposals to combat terrorism.
New legislation, the Criminal Justice (Terrorism and Conspiracy) Act and the Crime and Disorder Act, tightened up the laws dealing with terrorism and racism both of which have deeply affected the Jewish community, said Mr Straw.
He said: 'The government is committed to combating vigorously any manifestations of terrorist activity in the UK. We take the threat from foreign terrorists extremely seriously and we are determined that the UK should not be used as a basis for terrorism overseas.
The home secretary said that although anti-Semitic attacks had decreased recently, the number of racial attacks overall had increased.
He said: 'In addition, the new Crime and Disorder Act includes new racially aggravated offences which correspond to the existing main offences of violence, harassment and criminal damage.
'We amended the Bill to put it beyond doubt that where there is religious motivation alongside racial aggravation the case will be covered.'
However, Mr Straw added the government continues to monitor other areas of racial inequality and abuse including the continuing problem of Holocaust denial and racial abuse on the internet.
The UK, said Mr Straw, was a successful multi-racial society at the forefront of much anti discrimination legislation. The home office was also currently looking at proposals from the Commission for Racial Equality to update the Race Relations Act - part of an overall race relations strategy.
The government had already implemented several measures to cut racial inequality and was looking to implement others which to take this further including establishing a new grant to deal with racial disadvantage.
Mr Straw concluded: 'I intend to ensure that the government has a comprehensive and fully thought-out strategy for improving race relations and dealing with discrimination.'