Competition watchdog chief Gina Cass-Gottlieb says she would welcome new powers to break up big business, but her priority is strengthening Australia’s merger laws and new powers to tackle unfair practices, including by smartphone apps.

Opposition Leader Peter Dutton on Wednesday said the Coalition was working on a plan to forcibly break up the supermarket giants if they abused their market power, while Nationals Senate leader Bridget McKenzie said backing for new divestiture powers had been strengthened by big business’ support for the Yes campaign for the Voice.