Mark Thatcher remains under house arrest in South Africa after being accused of involvement in an alleged coup plot in Equatorial Guinea.
Sir Mark returned to his home after his Cape Town court appearance
Appearing in court on Wednesday, the 51-year-old was bailed to reappear on 25 November and ordered to pay a two million Rand (£165,000) bail bond.
Police say there is "credible evidence" he helped finance the alleged plot.
Sir Mark, son of former UK Prime Minister Margaret Thatcher, says he is innocent of all charges.
He is accused of violating laws banning South African residents from taking part in foreign military action.
Sir Mark was arrested on Wednesday morning at his home in the Cape Town suburb of Constantia.
Investigators were said to be examining his records and computers for information about the alleged plot.
Sipho Ngwema, spokesman for the South African police anti-fraud unit known as the Scorpions, told BBC's Newsnight police had "credible evidence" of Sir Mark's involvement.
He said Sir Mark had been arrested because of indications "he has contravened the Foreign Military Assistance Act of South Africa which prohibits South African residents from assisting in a coup or military activities outside South Africa without authorisation of the South African government".
"We allege he is one of the financiers of the coup to overthrow the government of Equatorial Guinea and we have received credible evidence that he has assisted financially in that regard," he added.
He said South Africa encouraged its residents to "export peace to neighbouring states and the rest of the continent".
"Anyone who is using this country as a springboard for violence and disorder, we are going to deal with those persons quite strongly," he added.
The act specified a fine or imprisonment for conviction, but not the severity, which is left up to the presiding officer, Mr Ngwema said.
He also said Sir Mark had been "planning to leave the country for good".
The investigator confirmed a report in Johannesburg newspaper This Day that Sir Mark had put his house on the market for 22 million rand (£1.8 million), sold four luxury vehicles and reserved flights for his wife and two children to the United States on Monday.
Mr Ngwema also confirmed that Sir Mark's children had been enrolled in American schools for the start of the new academic year in September.
Sir Mark said in a statement: "I am innocent of all charges made against me. I have been and am cooperating fully with the authorities in order to resolve the matter.
"I have no involvement in an alleged coup in Equatorial Guinea and I reject all suggestions to the contrary."
Speaking outside the court, Sir Mark's lawyer, Peter Hodes, said he had been held on suspicion of providing financing for a helicopter linked to the coup plot, and intended to plead not guilty.
On Wednesday, a spokeswoman for Baroness Thatcher said the former prime minister was on holiday in the United States and had not yet been contacted.
Charles Moore, her official biographer, described Sir Mark as a "very devoted son" who is extremely close to his mother.
Speaking on BBC Radio 4's Today programme, he added that the former prime minister is very "protective" of her son and is likely to find news of the arrest "extremely distressing".
Sir Mark's twin sister, Carol Thatcher, told BBC News 24 she was shocked by the allegations against her brother but that she had "lived through scandals before".
Speaking at Heathrow Airport, as she returned to London from Switzerland, she said she had not spoken to Sir Mark and did not know the details of the charges against him.
She said: "My real concern is for my mother because she's in America and I haven't spoken to her and I don't know her reaction and I care about her."
The alleged plot to overthrow the president of Equatorial Guinea has sparked dozens of arrests across Africa.
The alleged plot leader, former British SAS captain Simon Mann, an old Etonian turned leading African mercenary, has admitted trying to procure dangerous weapons - a charge which carries a possible 10-year jail sentence.