Zimbabwe's government has accused Australia of funding violence in an attempt to remove President Robert Mugabe from power.
Mr Howard accused Robert Mugabe of being a "grubby dictator"
In an interview, Zimbabwe's Information Minister Sikyaniso Ndlovu said Canberra was financing "terrorist activities" by channelling money to aid groups.
Australia is a vocal critic of Mr Mugabe and announced it was increasing funding to civic groups in Zimbabwe.
Relations were already bad after an Australian cricket tour was cancelled.
Announcing the tour boycott on Sunday over human rights concerns, Australian Prime Minister John Howard called Mr Mugabe a grubby dictator and said the "Mugabe regime at present is behaving like the Gestapo towards its political opponents".
Mr Ndlovu responded angrily in an interview with the Australian Broadcasting Corporation, accusing Mr Howard of acting in "Gestapo-like" fashion by banning the cricket tour which he said would have no effect in Zimbabwe.
Mr Ndlovu also warned that they would not tolerate any violence "by the puppets here who are funded by the Australian government".
"The monies that come to them are to cause violence - I've got a list, a long list of their terrorist activities here," he said.
Zimbabwe rejected an offer for the Australia cricket tour to take place in a neutral country.
This is the first time a government has acted to stop its cricketers travelling to Zimbabwe.