- Police Minister Bheki Cele says they have been "doing well" in dealing with cross-border crimes.
- He also said there would be random stop and search operations to ensure there was no trade in alcohol and tobacco.
- Home Affairs Minister Aaron Motsoaledi said there were 540 000 movements processed through SA's borders between 27 March and 13 July.
Minister of Police Bheki Cele says officers made a breakthrough this week with regard to the illegal transportation of alcohol from Mozambique to South Africa.
Speaking at the social cluster briefing on Wednesday afternoon, Cele said officers had also "made a big breakthrough on the crossing of illegal cigarettes from the neighbouring countries coming down here".
"I think we have been doing very well on that and it will continue," he said.
Cele said cross-border crimes are being dealt with by the country's law enforcement, in collaboration with Interpol.
On Sunday evening, President Cyril Ramaphosa suspended the sale of alcohol with immediate effect.
The sale of liquor was first banned under the hard lockdown Level 5 on 27 March, and then also during Level 4.
The ban was lifted on 1 June when the country moved to alert Level 3.
During Wednesday's briefing, Cele said: "There will also be random stop and search operations to ensure that the prohibition on the trade of alcohol and tobacco is not being subverted."
Meanwhile, following the implementation of travel restrictions to prevent the spread of Covid-19, Interpol has conducted an assessment, and said it was not enough.
According to Interpol, the land route from the Horn of Africa to SA has shown signs of activities, where the evasion of border control had, in some cases, taken a fatal toll on the lives of migrants.
However, Home Affairs Minister Aaron Motsoaledi says the study had not been brought to his attention.
From 27 March to 13 July, immigration officials facilitated nearly 540 000 movements through the borders, he said.
"Naturally, those who come illegally we can't know [of]. If we knew people who come to our country illegally, we would be able to arrest them, so nobody knows the number of people who could have crossed the borders illegally.
"But we know the number of those we have processed," Motsoaledi said.