The 23-year-old twins, Brandon-Lee and Tony-Lee Thulsie, appeared briefly in a Johannesburg magistrate court after being arrested at the weekend.
"It is alleged that they wanted to bomb the US embassy and Jewish facilities in the country," Hangwani Mulaudzi, spokesman for South Africa's elite police, the Hawks, told AFP.
The United States and Britain warned last month of possible imminent "terrorist" attacks by Islamic extremists in South Africa's major cities.
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The US warning said attacks could target sites frequented by US citizens, including high-end shopping malls in the economic hub of Johannesburg and Cape Town, which is popular with tourists.
The two men, who are accused of planning to join the Islamic State (IS) group in Syria, were remanded in custody and will return to court on July 19 to allow for further investigation.
"They had been on our radar since 2015. They tried to leave the country twice, through OR Tambo airport and through Mozambique (to join IS)," Mulaudzi said.
According to court papers, the brothers "conspired to commit the crime of terrorism by planning to cause explosions at a mission of the United States of America and Jewish institutions."
The suspects were also accused of inciting others to "aid and abet them", according to the provisional charge sheet.
"The incitement was to further the political, religious or ideological motives and objectives of... the Islamic State in Iraq and the Levant (ISIL)," it said.
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Two other suspects also arrested on Saturday were reported to be linked to the brothers. But the prosecution said they faced unrelated charges and were due to appear in a separate court later Monday.
Muslims account for only 1.5 percent of South Africa's 53 million people and the country has so far escaped the extremist attacks staged in several countries on the continent.
"We have got fairly verifiable evidence of South Africans going to the geographical Islamic State (in Syria)," Nick Piper of Signal Risk, a Cape Town-based security consultancy, told a press briefing recently.
"There is radicalisation happening within South Africa. There is a strong possibility that if an incident does happen, it will be a South African."
The US embassy declined to comment.
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