South Africa has deployed more than 3 000 soldiers nationwide to bolster security and support police this month during anti-migrant protests that organisers have vowed to hold every week, a letter signed by the president showed on Friday.

Protesters marched ​across cities on Tuesday, with some demonstrations hit by violence, and an anti-migrant movement says it will march again every Thursday to press its demands for the government to take a tougher stance on undocumented foreign nationals.

In the letter sent to the parliamentary speaker, President Cyril Ramaphosa said the deployment of 3 405 members of the South African National Defence Force (SANDF) began on June 28 and would cost an estimated 54.6-million rand ($3.37-million).

"Members of the SANDF ... will be on standby for any eventualities," said the letter, which was published by parliament.

Thousands of demonstrators draped in national flags, some wielding wooden weapons, took to the streets on Tuesday. The protests were mainly peaceful, but a handful descended into violence and looting of shops.

Police arrested more than 900 people for offences including immigration violations, public violence, robbery and harbouring undocumented migrants. Soldiers were deployed to an inner-city part of Johannesburg where many migrants stay.

The protests followed months of unrest that have drawn international criticism as foreigners have been driven from their homes and seen their businesses and property vandalised.

Immigrants are blamed for taking jobs, driving crime and putting pressure on public services, claims that social ​scientists say lack evidence.

The immigrant population stands at about 3-million or about 4% of the total, according to StatsSA, a relatively low share by global standards.