He said that immigrants were "prepared to work at lower wages".
"Therefore many black South Africans feel that these people are robbing them of their jobs and of their food and of their livelihoods so I think that's the main root cause," he said.
He said that crime could not be solely blamed on foreigners.
"But there's no doubt that a substantial percentage of the illegal immigrants are involved in the high crime rates which we have."
He rejected that claim that the legacy of apartheid was to blame for many of the country's current social problems.
Under apartheid, people were deprived of their full political rights, but not on a "socio-economic basis", he said.
"It was quite developmental if you look at what has happened in the educational field, in the field of housing - I'm now talking from the 1960s to the 1990s, the establishment of new universities, the creation of opportunities, small business development," he said.
Critics of apartheid have argued that black South Africans at the time received an inferior education - many young people boycotted school to fight apartheid - and black ownership of commercial business was prohibited or highly regulated.
Apartheid is often blamed as a means of "political expediency", Mr De Klerk said.
I think Zimbabwe's lot is now in the hand of Zimbabweans
FW De Klerk
"But there's no doubt that we've now had a new full open democracy since 1994 - it's almost 15 years - and month by month the claim that everything which is wrong is to be blamed on the past loses its appeal and its credibility."
In a statement on Thursday, the government acknowledged "the urgent need to accelerate its programmes for alleviating poverty, unemployment and other forms of socio-economic deprivation".
It also appealed to communities "to reject any agitation from those who wish to reduce this country into a lawless country".
'Up the garden path'
With regard to the political crisis in Zimbabwe, Mr De Klerk said that South Africa's reputation had been "damaged".
The Cape Town mayor wants local government to co-ordinate relief
Efforts by Thabo Mbeki, South Africa's current leader, to get a unity government between President Robert Mugabe's party and that of opposition leader Morgan Tsvangirai were "outdated", he said.
"At certain stages President Mugabe made promises to President Mbeki which he didn't keep - and in that sense I'm a bit sorry for President Mbeki because I think at times Mugabe led him up the garden path."
He also had praise for Mr Tsvangirai and his "statesmanlike qualities" in agreeing to an election re-run.
"I think Zimbabwe's lot is now in the hand of Zimbabweans," he said.
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