The government should build a new publicly owned bank to service regional towns and jack up the major bank levy to help underwrite “community branches” that provide in-person banking services on behalf of multiple institutions in remote areas, a Senate probe has found.

The biggest banks should also be forced to enter deals with Australia Post to provide banking services via post offices in the bush, the inquiry said, with ANZ the only big four lender still without a contract to facilitate this via the Bank@Post program.