The exercise of the two-well option takes the joint venture's current drilling campaign with the Transocean Legend in Western Australia's Browse Basin to four wells.
The semi-submersible drilling rig is currently drilling its first well, Kontiki-1, and on Friday was drilling ahead at 3237m towards a depth of 4160m.
Kontiki-1 is targeting potential resources of up to 5 trillion cubic feet of gas and is about 29km northwest of the JV's first well, Poseidon-1.
Following the completion of Kontiki-1, the Transocean Legend will move to drill the Poseidon-2 appraisal well.
The JV secured the Transocean Legend in June for a minimum term of 148 days after Transocean cancelled its agreement with Oilex to drill exploration wells in the Timor Sea in the third quarter
The partners began searching for a new rig after the Sedco 703 rig's American Bureau of Shipping survey expired on May 28.
The JV has a further option to drill an additional four wells before the end of the drilling contract with Transocean.
ConocoPhillips is operator of the Browse Basin drilling program, which spans three permits: WA-314-P, WA-315-P and WA-398-P.
The company holds a 51% interest in WA-314-P and WA-315-P, and a 60% interest in WA-398-P.
Karoon holds the remaining stakes in the three permits.
See ConocoPhillips at SEAAOC which runs from September 9-11 in Darwin.