The ANC Youth league has demanded that land owned by private individuals and companies be made available to house the Western Cape's poor.
This was the first of nine demands contained in a memorandum delivered to the Western Cape government following a protest on Monday.
"There are white people who don't even live in South Africa. They live overseas. Yet, they own land in our country. Without land we can't fight for the economy we want," ANCYL Dullah Omar region president Khaya Yozi said as he read the memorandum over a loudspeaker.
Yozi singled out Constantia and the Rondebosch Common as land that could be given to the province's poor.
More than a thousand protesters, most of them affiliated to the local ANCYL, the provincial ANC, the Young Communist League (YCL), the Congress of SA Trade Unions (Cosatu), and the ANC Women's League assembled outside the Western Cape legislature.
They demanded that premier Helen Zille accept the memorandum of service delivery demands and refused to give the document to sports and recreation MEC Ivan Meyer instead.
"We want Zille. We want the madam," the crowd chanted.
They later allowed economic development MEC Alan Winde to sign the memorandum, but expressed outrage that Zille had snubbed them.
Winde was booed when he tried to explain that the document would be handed to the premier.
Last week, Zille said she would receive the memorandum only if the ANCYL retracted threat to make the city ungovernable.
On Monday, ANCYL spokeswoman Magdalene Moonsamy said this would not happen.
"We will never apologise to the madam, to Zille. The days of apartheid are over. They want to charge us, but we'll charge Helen Zille for genocide in the Western Cape."
The ANCYL blamed Zille for the loss of life in Khayelitsha and its surrounds during violent service delivery protests, insisting that the provincial government's failure to deliver had forced people to take to the streets in anger.
ANC Western Cape deputy chairman Abe Bekeer told cheering supporters the Democratic Alliance, which runs the province, would be ousted after the 2014 elections. He called on demonstrators to show restraint and to remain disciplined.
Cosatu provincial secretary Tony Ehrenreich said all its workers in the province would be called on to add to the pressure on Zille to change the DA's approach, specifically when it came to housing in affluent areas in the Cape Peninsula.
"It won't be long before we live in Constantia, Rondebosch and Sea Point. Cosatu is waiting for Helen Zille to take us seriously. She is hiding behind police. We must make sure we're back here again," said Ehrenreich.
Police officers in full riot gear blocked the entrance to the Western Cape legislature, while members of the police's intervention unit stood at the nearby St George's Cathedral.
A police helicopter hovered over the city centre for a few hours.
Protesters dispersed peacefully, but vowed to return to settle their disagreements with Zille face to face.