Baroness Thatcher remained in a stable condition overnight in St Thomas' Hospital, in central London, the hospital said.
The 82-year-old former Prime Minister was admitted to the hospital on Friday night and was said to be undergoing medical checks.
On Saturday morning a spokeswoman for the hospital said: "Baroness Thatcher has remained stable overnight and we have nothing further to add at this stage."
It was reported Lady Thatcher was taken to hospital by car.
Two red Metropolitan Police cars were parked just outside the main entrance of St Thomas' Hospital in Lambeth Palace Road on Saturday morning.
It was not clear whether this or any other extra security was in place for Lady Thatcher.
Lady Thatcher very rarely speaks in public, following advice from her doctors, but she does still sometimes say a few words at private functions.
Friends say she is lucid most of the time but occasionally drifts off in the middle of conversations because of difficulties with her short-term memory.
Earlier this month she urged Conservatives to "hold firm to their beliefs" as she was honoured with a statue at the party's HQ.
Lady Thatcher was prime minister from May 1979 until her resignation in November 1990. She was Britain's first woman prime minister and the first leader to win three elections in a row.