In a press conference in the early hours of Monday, Pashinyan said his Civil Contract party had prevailed, calling it a "historic victory".
Armenia's election commission had released early results from about 21 per cent of polling stations by the time Pashinyan gave his press conference.
Sunday's vote, Armenia's first general election since a crushing military defeat by Azerbaijan in 2023, was viewed as a test of Prime Minister Nikol Pashinyan's push to deepen ties with the West and secure a peace deal with Azerbaijan after years of conflict and political turbulence.
The early results showed Civil Contract clinching 54.5 per cent of the vote and pro-Russian Strong Armenia alliance in second place, with 21.9 per cent of the votes.
The Armenia Alliance was in third place with 8.7 per cent, and the Prosperous Armenia party was trailing in fourth with roughly five per cent.
Turnout in the landlocked country of three million was strong at nearly 59 per cent of eligible voters. The Central Election Commission is expected to announce official preliminary voting results on Monday.
Pashinyan's Civil Contract, which has brought Armenia closer to the West since taking power in 2018, squared off against three main pro-Russian opposition parties.
His key rival is Samvel Karapetyan, who founded Strong Armenia last year and campaigned on a pro-business platform and a pledge to maintain Armenia's close ties to Russia.
A strong showing for Pashinyan would give him a mandate to conclude peace negotiations with Azerbaijan, which has been at war with Armenia intermittently since the late 1980s, and to normalise relations with Turkey, a key ally of Azerbaijan.
