Results from the elections have not been finalized, but Peter O'Neill said he would be able to form a ruling coalition after his party emerged as the most popular in the vote and four other parties gave their support.
"I can assure our people and the country we have the numbers to form government," O'Neill told reporters.
His party was openly backed late Tuesday by his leadership rival and political veteran, Sir Michael Somare. Papua New Guinea was plunged into political chaos last August when Parliament elected O'Neill prime minister in place of Somare, who was in Singapore undergoing medical treatment.
The Supreme Court ruled in May that Somare was the rightful leader, but O'Neill refused to cede power. Two of the three judges who made the ruling were later charged with sedition.
O'Neill's People's National Congress appeared to be gaining the most seats in elections held from June 23 until July 6. The electoral commission said his party held 20 of the 66 seats declared by Wednesday with 45 races still being counted.
O'Neill needs the support of a majority of the 111 seats in Parliament to become prime minister.
Somare, who was first elected prime minister when Papua New Guinea became independent of Australia in 1975, said the five lawmakers in his own party would join O'Neill's coalition.
Another former prime minister, Sir Julian Chan, declared the six lawmakers in his own party would support O'Neill. Former prime minister Pias Wingti, the only member of his party so far elected, also backed O'Neill.
O'Neill said his coalition would be joined by the Triumph Heritage Empowerment Party, which is in a strong position to win as many as 12 seats.