Jones said the threats had come from people who did not listen to 2GB.
"The radio station has conducted research over the past weekend and it's clear that the great majority of listeners to this program acknowledge my apology and have not changed their attitudes,'' he said.
"We saw that last week in the avalanche of calls made to this program.
"But as (2GB executive chairman) Russell Tate said in his statement yesterday, we are now witnessing 21st century cyber bullying.''
Jones said he did not object to petitions.
"They have been a reality for years.
"But one petition calls on signatories to 'destroy the joint'.''
It was not immediately clear if that was a reference to Jones' comments in August in which he suggested Ms Gillard and other women were "destroying the joint''.
The threats had been made on websites, including Facebook, by email to the radio station and via its telephone switchboard.
Some of the telephone calls had reduced the "girls on the switchboards'' to tears, Jones said.
- AAP