Western Cape premier Helen Zille said on Friday that she would personally receive a memorandum from ANCYL members during their march next week.
"I have undertaken to receive the ANCYL's memorandum personally on condition that they withdraw their threats to make the city ungovernable," she said in a statement.
"[They must]... apologise to the people of Cape Town for the loss of life and damage to property caused during their previous 'ungovernability campaign'."
The African National Congress Youth League is scheduled to march to the provincial legislature in Cape Town on Monday as part of a campaign for "economic freedom" in the province.
Zille, who is also the leader of the Democratic Alliance, said she spoke to provincial police commissioner General Arno Lamoer and the city's community safety director Richard Bosman and was assured that "law and order" would be maintained during the march.
"General Lamoer and Mr Bosman assured me that the plans of the police and metro police are in place and that all necessary steps will be taken to prevent intimidation and disruption of public transport," she said.
"Anyone breaking the law will be summarily arrested and charged. The march organisers will be held financially and personally liable for any damage to property."
The City of Cape Town said on Friday that it had approved the ANCYL's march.
The marchers were told to assemble at Kaizergracht street from 10am on Monday morning. The march would start at 11am and move along Darling Street, left into Adderley Street, and then to the provincial buildings in Wale Street.
"The demonstrators should commence their return along the same route originally followed by no later than 1.30pm," it said.
"Also, according to the stipulations, the march must respect and observe all relevant laws and municipal by-laws relating to nuisance, use of loudspeakers [and] traffic... at all times."
The city had appointed marshals to supervise the marchers.
The ANCYL would be joined by the Congress of SA Trade Unions, the SA Students' Congress, the SA National Civic Organisation, the Congress of SA Students, the Islamic Unity Convention, and taxi organisations.