Foreign Minister Alexander Downer said going ahead with the national team's tour planned for May would "send the wrong message" to both Zimbabwe and neighboring South Africa, a strong Mugabe ally.
"We'd rather it didn't go ahead, obviously the Zimbabwe government would be pleased if it did," Downer told commercial radio in Melbourne.
Australian Prime Minister John Howard spearheaded moves to suspend Zimbabwe from the 54-nation Commonwealth after Mugabe was re-elected last March in polls widely deemed to have been fraudulent.
Howard and his British counterpart Tony Blair successfully countered efforts led by South Africa and Nigeria to obtain Zimbabwe's re-admission to the Commonwealth during a group summit meeting in Nigeria in December.
Last week, Cricket Australia (CA), the sports governing body in the country, said it would not let "moral issues" stand in the way of the May tour of Zimbabwe.
"Safety and security is the key issue for us on any overseas tour and we have always said the broader issues to do with moral issues should be left to those who are elected to discuss those issues," Cricket Australia spokesman Peter Young said.
Australian cricket officials and players' representatives will visit Zimbabwe in March to look at the country's security measures, he said.
Cricket Australia's stance contrasted with a report issued earlier this month by England and Wales Cricket Board (ECB) official Des Wilson saying concerns over Mugabe's human rights record should be considered when the Board decides next month whether to proceed with a national tour planned for November.
Downer said the final decision about whether the Australian tour should go ahead was up to cricket authorities. "They will have to make a decision in the end and we will leave the decision to them," he said.
Australia cancelled a tour to Zimbabwe in 2002 because of safety concerns following troubled national elections. But it played one match in the country last year as part of the World Cup tournament.
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