Zambian justice minister announced the consultation, which will run until Friday, in a speech to parliament last week.
South Africa recently revoked its planned departure from the ICC, based in The Hague, and The Gambia's new president, Adama Barrow, reversed his predecessor's decision to withdraw.
Zambian justice minister Given Lubinda announced the consultation, which will run until Friday, in a speech to parliament last week.
"The consultative process will be conducted through public hearings in 30 districts where members of the public will be invited to make oral and written submissions," Lubinda said.
The government will then decide whether to seek to leave the court, and plans to announce its decision at an African Union assembly later this year.
The court has been hit by withdrawal threats following longstanding complaints of an alleged bias against African nations.
One Zambian opposition leader accused President Edgar Lungu of trying to evade justice by seeking to leave the court.
"President Lungu thinks that by running away from ICC he cannot face the ICC," said Nason M'soni, of the MMD party.
Opposition parties accuse Lungu of electoral fraud and political violence during his 2016 re-election campaign, though the result was upheld by the courts.