An alliance led by his rival, ex-leader Robert Kocharyan, came second with 21 percent, according to the results based on ballots from 100 percent of precincts counted.
A winning party or bloc needs to obtain at least 50 percent of seats plus one and can be assigned additional seats in order to form a government.
Pashinyan hours earlier claimed victory based on early results, but Kocharyan's grouping swiftly contested the vote and alleged election fraud.
A record four electoral blocs and 21 parties ran for election on Sunday.
The vote was seen as a two-horse race, with both Pashinyan, 46, and Kocharyan, 66, drawing massive crowds in the run-up to the polls.
"The people of Armenia gave our Civil Contract party a mandate to lead the country and personally me to lead the country as prime minister," Pashinyan announced in the small hours of Monday.
"We already know that we won a convincing victory in the elections and we will have a convincing majority in parliament," he added, urging supporters to turn up at Yerevan's main square Monday evening.
Kocharyan's electoral bloc said it would not recognize Pashinyan's quick claim to victory, which came when around 30 percent of precincts had been counted.
"Hundreds of signals from polling stations testifying to organized and planned falsifications serve as a serious reason for lack of trust," the bloc said in a statement, adding it would not "recognize" the results until the "violations" were studied, AFP reported.
On Sunday evening, the general prosecutor's office said it had received 319 reports of violations. It said it had opened six criminal probes, all of which concerned bribes during campaigning.
The vote was followed by Russia, arch-foe Azerbaijan and Turkey, which backed Azerbaijan in the six-week war over the breakaway region of Nagorno-Karabakh last year.
Despite stifling heat, nearly 50 percent of around 2.6 million eligible voters cast their ballots, election officials said. Some observers said turnout in the South Caucasus country of three million people was higher than expected.
During a campaign marred by polarizing rhetoric, Pashinyan had said he expected his party to secure 60 percent of the vote. Some pollsters had called that estimate far-fetched.
Election officials said the vote was conducted in accordance with Armenia's legislation.
Kocharyan was himself accused of rigging a presidential election in favor of his hand-picked ally and presiding over a deadly crackdown on protesters in 2008.
Armenia won international praise for holding its first free and fair vote under Pashinyan in 2018.
On the streets of Yerevan on Sunday, Armenians voiced conflicting opinions about Pashinyan.
Voter Anahit Sargsyan said the prime minister, who spearheaded peaceful protests against corrupt elites in 2018, deserved another chance.
She said she feared the return of the old guard whom she accused of plundering the country.
"I voted against a return to the old ways," said the 63-year-old former teacher.
Another voter, Vardan Hovhannisyan, said he had cast his ballot for Kocharyan, who calls Russian leader Vladimir Putin his friend.
"I voted for secure borders, solidarity in society, the return of our war prisoners, the well-being of the wounded and a strong army," said the 41-year-old musician.
Critics blame Pashinyan for having ceded territory in and around Karabakh to Azerbaijan in a humiliating truce agreement, and accuse him of having failed to deliver reforms.
Pashinyan has said he had to agree to the Moscow-brokered peace deal with Azerbaijan in order to prevent further human and territorial losses.
More than 6,500 people were killed in the war, according to the latest official figures from Armenia and Azerbaijan.
Besides Kocharyan, who hails from Karabakh and was in power between 1998 and 2008, two other leaders of post-Soviet Armenia backed parties in the race.
During a venomous campaign, candidates exchanged insults and threats. Pashinyan brandished a hammer at rallies, while Kocharyan said he would be ready to fight the prime minister in a duel.