The well is at a depth of 3202m and attempts are being made to recover the lost wireline logging tool.
Oil Search will make a decision on its forward program once the final logs are finished.
Cobra-1A is primarily directed at the Iagifu sandstone - the principal reservoir in PNG's Gobe and SE Gobe fields - in a seismically defined sub-thrust prospect.
Oil Search said Cobra-1 is the first well in PNG to target a sub-thrust play as the primary target.
Participants in Cobra-1A are operator Oil Search (62.556%), Murray Petroleum (26.497%) and Cue Energy (10.947%).