Karim al-Nuri, a top leader from the Badr militia and the spokesman of the volunteer Popular Mobilisation units, said it would take no more than "72 hours" to flush out holdout IS fighters.
The Popular Mobilisation units account for the bulk of the manpower involved in the two-week-old operation to wrest back Tikrit, alongside army, police, militia and tribal forces.
The last IS fighters holed up in the city centre are "surrounded from all sides", Nuri said.
Nuri added that the liberation of Tikrit would only be announced once a path has been cleared through the thousands of bombs the jihadists have planted to defend the city.