The country's Prime Minister Peter O'Neill, of the People's National Congress party, said on Saturday the elections were calm and peaceful despite some voter complaints.
Meanwhile, Moresby Northwest MP Michael Malabag denounced the Electoral Commission for the delay in counting votes, which he labelled a "bloody big joke", according to the Post Courier newspaper.
The elections were postponed for three days in the capital, Port Moresby, because of a strike by officials.
A student group also raised a complaint to the commission over insufficient ballot papers at the University of Technology in the city of Lae, the second most populated city in the country, where they were registered to cast their votes.
The election will decide the fate of 111 seats of the unicameral parliament and 3332 candidates, out of which only 165 are women.
O'Neill, 52, is competing with former prime ministers Michael Mamare and Mekere Morauta, as well as with Don Polye and his Triumph Heritage Empowerment Party.
The government of O'Neill has been accused by its political rivals of corruption and ruining the country that has a population of around seven million people.
No political party in Papua New Guinea has ever won an absolute majority in the past and experts do not anticipate any change in the trend this time, despite there being no opinion polls carried out among voters.
