March and March had previously set June 30 as the deadline for undocumented immigrants to leave the country voluntarily.
March and March leader Jacinta Ngobese-Zuma announced that supporters will take to the streets every Thursday until the government takes action to remove undocumented immigrants from South Africa.
Addressing protesters outside SAPS Point in Durban on Tuesday after thousands marched through the city, Ngobese-Zuma said the campaign would continue weekly until government responded to their demands.
"For as long as they haven't left, we are marching every Thursday," she told supporters.
She also warned that if authorities continued deploying large numbers of police officers to monitor the demonstrations, the cost to the state would continue to rise.
