Auckland's mayor says the council has not been able to find an affordable way of stopping a controversial demolition of three historic houses in the suburb of St Heliers.
The 1930s art deco buildings on Turua Street are the first to be removed to make way for a retail centre in a move opponents say will ruin the character of the seaside village.
Protesters stood watch outside the houses on Monday, saying they have been tipped off that demolition will resume this week and will continue to fight to save them.
Work was suspended in December last year after mayor Len Brown stepped in and asked for time to consider other options.
However, Mr Brown says the council has found that saving the houses by buying the land from the developer would be hugely expensive, costing about $10 million.
The mayor says Auckland's new council inherited the situation from the former council and it is too late to do anything.
Protesters want the council to issue a heritage order to protect the houses.