He said the comments were "very disappointing".
"I have two daughters, so you can expect that's how I would feel personally about it."
Now Australia's ME Bank has announced it has pulled its advertising from Jones' show.
Australian media outlet Adnews reported ME saying it had removed its advertising because it took Jones' comments very seriously and they didn't reflect the bank's values.
ME - which is owned by Australian superannuation funds - said its customers had been contacting it to urge it to withdraw support for Jones.
Jones made his comments while Morrison and Ardern were at the Pacific Islands Forum in Tuvalu where island leaders are calling for action on climate change.
Ardern had said Australia had to "answer to the Pacific" on climate change.
Jones then called Ardern a "joke" for preaching about the issue.
But Fiji Prime Minister Frank Bainimarama also hit out at Jones.
"Easy to tell someone to shove a sock down a throat when you're sitting in the comfort of a studio. The people of the Pacific, forced to abandon their homes due to climate change, don't have that luxury," he said.
"Try saying it to a Tuvaluan child pleading for help."
Malcolm Turnbull, the former prime minister of Australia, said Jones should apologise to Ardern for his latest "misogynistic rant".
Activist group Sleeping Giants Oz wants socks sent to the chair of Nine, Peter Costello. Nine owns 2GB.
Jones later issued an apology, but it proved short-lived as he subsequently launched into a fresh attack on Ardern, calling her "gormless" and a hypocrite.
"It's easy to run around the world, smile at people and look good and hug people and all the rest of it," he told Newstalk ZB yesterday.
Returning to the air on Friday, Jones continued his attack, saying Ardern's position on climate change was "ignorant and stupid" and she had acted hypocritically.
He then called the climate discussion a "hoax" before saying Australia's actions on the issue would make no difference when compared to China's emissions.
"What is the gormless Ardern going to say today to China?" Jones asked.
It came as Australia faced increasing pressure from other members of the Pacific Islands Forum to take more action on climate change.