Somare has been battling serious health conditions since April and the 75-year-old leader is yet to announce his own resignation or be removed from this role through the processes set out in the constitution.
While Somare chose Abal as his successor before he took medical leave, Abal's subsequent moves to oust O'Neill, Don Poyle and William Duma from their key ministerial portfolios over recent months have stirred up resistance.
With parliament resuming yesterday, a vote on a new leader received 70 votes for O'Neill compared to 24 for Abal according to The National, which reported that O'Neill was Papua New Guinea's new Prime Minister.
Various media outlets around the world have followed this theme, but in a separate report Abal told The National the vote was an illegal move orchestrated by the opposition and "facilitated by" Speaker Jeffery Nape.
"It's sad (that the) democratic process was hijacked," he told The National.
"The speaker has been known for such pursuits - not following laws."
Abal will take the necessary legal action.
Under the context of Somare's ill health, the constitutional processes dictate that two appointed medical practitioners will need to provide a medical report to the governor general who could then decide whether parliament needs to elect a new prime minister.
With the two physicians appointed, Abal reportedly said this medical report would be provided in 28 days.
The National Alliance party has long led a Coalition government under Somare and won 27 out of 109 seats in parliament in the last election, with the next election expected in June 2012.
O'Neill hails from the People's National Congress party, while the National Alliance party has conflicting allegiances between Polye and Abal.