JOHANNESBURG, May 31 (Reuters) - A wave of attacks on foreigners in South Africa has killed 62 people since the violence broke out three weeks ago, police said on Saturday.

The violence, which has now subsided, targeted newcomers to South Africa as well as those who had been in the country for decades, and tens of thousands were forced to take refuge in shelters around the country.

"This has raised the earlier toll of 56 dead. A total of 670 have been injured," police spokeswoman Sally de Beer told the SAPA news agency. Some had died in hospital from injuries.

Fifty-two of the dead were from Gauteng province, the heart of South Africa's economy, where the attacks began on May 11 before spreading to KwaZulu-Natal and Western Cape.

De Beer said no major attacks had been reported recently in the violence that targeted mainly Zimbabweans and Mozambicans.

Competition for housing and jobs combined with soaring food and fuel prices are believed to have been behind the riots. Unemployment in South Africa is around 24 percent.

At least 50,000 Mozambicans and Zimbabweans have left South Africa as a result of the unrest.

Zimbabweans, whose country is in economic meltdown, are the largest immigrant group in South Africa, accounting for 60 percent of the 5 million migrants living in the country of about 50 million.

Relief agencies and U.N. officials say they are shocked at conditions in the shelters where thousands of migrants now live. Many are sleeping outside in temperatures that drop to near freezing at night.

Government assistance to the refugees has been disappointing, they say, with most blankets, clothes, food and medical supplies coming from non-governmental groups and individuals. (Reporting by Phumza Macanda; Editing by Giles Elgood)

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