Nelson Mandela’s body is lying in state at the Union Buildings, where he was sworn in as South Africa’s first black president in 1994.
More than 50,000 people were waiting for buses when the warning came.
Nelson Mandela will be buried at his ancestral home in Qunu on Sunday, December 15. He died on December 5 at the age of 95.
His body is to be flown to the rural area of the Eastern Cape where he grew up.
Friday is the last of three days for people to file past the body in Pretoria.
The government said it could not guarantee everyone already waiting for buses would get in.
The response from the public to view Nelson Mandela, known by his clan name Madiba, had been “overwhelming and heart-warming”, government spokesman Phumla Williams said in a statement.
Between 12,000 and 14,000 people had paid their respects to Nelson Mandela on the first day he laid in state “with two people passing every three seconds on day two”, she said.
If any additional numbers came on Friday it would make it physically impossible for people to get the opportunity to file past the body, she added.
“We appeal to members of the public who have not had the opportunity to pay their respects to President Mandela at the Union Buildings, to say goodbye in their own personal way.”
Correspondents who have visited the coffin said Nelson Mandela’s body could be seen through a glass screen, dressed in one of his trademark patterned shirts.
At each end of the casket stood two navy officers clad in white uniforms, with their swords pointing down.
Some mourners stopped briefly to pray, while a number of people reportedly fainted.
At the end of the day, Nelson Mandela’s body will be returned to One Military Hospital before being flown from Waterkloof Military Airbase near Pretoria to Mthatha on Saturday.
Lt-Gen Xolani Mabangu, from the defense force, said chief mourners among the Madiba clan and Mandela family, as well as senior government officials, would accompany the body, the South African Press Association reports.
A military guard of honor will welcome the arrival, and the coffin will be placed on a gun carriage and transported to a hearse.
Nelson Mandela’s body will then be taken to his home village of Qunu, where the Thembu community will conduct a traditional ceremony.
A national day of reconciliation will take place in South Africa on December 16, when a statue of Nelson Mandela will be unveiled at the Union Buildings.
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