In a development that raises the likelihood of potentially fractious ANC-led minority governments in some of the country’s biggest municipalities, coalition talks between opposition parties have collapsed.

In a news conference on Tuesday, the DA stopped short of conceding the City of Johannesburg, but went as far as to say its pathway to regaining the mayorship of the metro is narrow after this week’s announcement that a smaller party, the Patriotic Alliance, has struck a deal with the ANC...