Daily protests, road blocks and the closure of minibus routes – which are vital for many workers – have closed shops and businesses and left hospitals short staffed.
Protesters torched buses and threw stones, while the disruption kept about 450,000 schoolchildren at home.
The dispute began as a local clash between city authorities and taxi drivers over impounded vehicles, but has now escalated to a national incident after the central government accused the city of acting outside the law.
A police officer and an unnamed 40-year-old British citizen are among the dead, officials said. The South African National Taxi Council (Santaco) began the one-week shutdown last Thursday in protest at a new municipal law allowing city authorities to impound vehicles for offences such as driving without a licence or registration plates.
Taxi drivers alleged the authorities were deliberately targeting them and impounding vehicles for minor infractions that might earn other drivers only a fine. City authorities have accused taxi “mafias” of spreading violence as a negotiating tactic while the municipality tries to clean up the industry for the safety of commuters.
At least seven city buses have been torched in the past week.
"In Cape Town, violence will never be tolerated as a negotiating tactic. We reiterate our call on Santaco to return peacefully to the negotiation table," said Cape Town city mayor Geordin Hill-Lewis.
Minibus taxis are a mainstay of transport for many in South Africa and the network completes an estimated 1.5 million passenger trips each day in the Western Cape province, which includes Cape Town.
African National Congress transport minister Sindiswe Chikunga accused Cape Town, which is run by the opposition Democratic Alliance party, of being arrogant and snubbing negotiations.
She said its tough new sanctions for road traffic infringements were at odds with national laws. All minibus taxis seized under such circumstances should be immediately released and the city should return to the negotiating table.
“To this end, we call on the city to return to the negotiating table to address the areas of disagreement and demonstrate a genuine effort to find a lasting resolution to the current challenges,” she said.
Mr Hill-Lewis defended the city's actions, saying the vehicles' seizures were being conducted according to national laws.
“Well, if by arrogant she means we are not prepared to negotiate with people who are holding a gun to the city’s head, and going out there and perpetrating acts of violence and intimidation and mayhem on the city’s streets – then so be it."
Santaco has distanced itself from the violence, which it said was fuelled by protesters, not its members.
About 120 people have been arrested during the disturbances, according to police, who said there had been incidents of looting, stone throwing and arson. The UK issued a travel alert warning tourists to be careful of the strikes.
President Cyril Ramaphosa was forced to shift a major Cape Town speech he had been due to deliver on Wednesday to mark international women's day. The venue was changed to Pretoria instead.
By Wednesday morning, a public holiday, routes in the city were running smoothly and there were no reports of violence. Disruption to supplies meant supermarkets had cancelled deliveries and some stocks were running low.