After counting over 99 percent of the votes, the PAS received 49.91 percent. In second place was the opposition Patriotic Electoral Bloc (BEP) with 24.33 percent, according to information from the electoral commission.
According to the BBC and the news agency Moldpres, the ruling party secured 54 seats in the 101-member parliament.
Other forces likely to enter parliament are the pro-European Alternative bloc (8 percent) and the populist Our Party (6.2 percent).
The official final result is expected on Monday.
Maintaining a parliamentary majority would enable PAS to continue the process of Moldova's accession to the EU, which requires years of legislative reform.
PAS representatives described this election as the most important since independence. The election campaign was marked by mutual accusations of fraud.
President Maia Sandu warned of Russian attempts to influence the election through disinformation and vote buying. Her national security adviser, Stanislav Secrieru, said the election infrastructure and government websites had been the target of cyberattacks, and there had also been false bomb threats. Moscow denied any involvement.
The co-chair of the Patriotic Bloc, Igor Dodon, called for protests in front of parliament on Sunday and accused Sandu of wanting to annul the election, but provided no evidence. Shortly before the vote, two pro-Russian parties were removed from the list of candidates on suspicion of illegal financing.
(reuters, est)