Nepal has already held local elections this year electing local bodies across the country. Oli was projected as the Prime Ministerial candidate by the two parties when they chose to form an alliance and contest the poll under a common manifesto.
The ruling Nepali Congress, which was the largest party in the last election, won only 10 seats, according to tallies.
An official from the election commission pours the ballot papers from the box, as officials start counting the votes, a day after the parliamentary and provincial elections in Kathmandu, Nepal December 8, 2017.
A total of 1,663 candidates contested polls for parliamentary seats. Two Madhesi parties have won five seats.
There are 165 seats to be decided on a first-past-the-post basis for which voting was held on Thursday with another 110 seats decided by proportional representation.
Ayodhee Prasad Yadav, Nepal's chief election commissioner, estimated voter turnout at 67 percent and said there were no major problems.
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The commission said the November 26 and December 7 elections to the House of Representatives and the provincial assemblies represented a key milestone in the implementation of the 2015 Constitution. The RJPN, however, is faring better than the Forum-Nepal.
The European Union has deployed more than 100 observers at 633 polling centres across the country for the voting process.
A leftist alliance between Nepal's former Maoist rebels and moderate communists appeared to be heading for a victory in elections aimed at completing a transition to democracy after the abolition of the monarchy and end to civil war.
Nepal has seen 10 government changes in as many years.
In 2015, when Nepal adopted a new Constitution that split it into seven states, dozens of people were killed in ethnic clashes over territory and rights.
Protests by ethnic groups in southern Nepal who complained they did not get enough territory in the province assigned to them had turned violent and left some 50 people dead.