The company said the first well, Cook-1, has reached a total depth of 3140 feet, with logs suggesting multiple reservoir quality zones, with possible hydrocarbons, have been encountered.
AusTex said it would decide whether to complete the well depending on further analysis by drilling contractor Halliburton.
The drilling rig has now moved northeast to the Lancaster-1A well site to examine a structural high defined by seismic.
AusTex is paying for the drilling with funds raised from its $20 million initial public offering late last year.
AusTex Oil owns six leases held by International Energy Corporation - a wholly-owned United States subsidiary - which contain 6.1 million proven recoverable barrels of oil.