The drill stem became stuck in the Habanero-2 well at a depth of 13,753ft (4193m), 32ft off the bottom.
Geodynamics is currently obtaining expert advice on options to overcome the setback, the company said today.
Specialist equipment to pursue some of the options has been located and mobilised to site.
A decision as to how to proceed with the recovery program is expected to be made in the next few days with the company announcing its forward plan later this week.