State-run IRNA news agency and state TV said early Sunday that 1,960 from 5,000 ballots in Tehran had been counted, based on an Interior Ministry report updated hourly.
Officials have not yet released turnout figures from Saturday's election. However, IRNA said it was 41%, based on unofficial reports.
In the last parliamentary election in 2019, only 42% of eligible voters cast a ballot in what was considered to be the lowest turnout since the 1979 Islamic Revolution.
High-profile moderates and conservatives stayed away from Friday's election and reformists called it neither free nor fair as it was mainly a contest between hardliners and low-key conservatives loyal to Islamic revolutionary ideals.
Mohammad Khatami, Iran's first reformist president, was among critics who did not vote on Friday.
Hassan Rouhani, a pragmatist who was elected president in landslide wins in 2013 and 2017 promising to reduce Iran's diplomatic isolation, was banned from running, drawing criticism from moderates.
Hard-liners have controlled the parliament for the past two decades — with chants of "Death to America" often heard while in session.
Under Iranian law, the parliament has a variety of roles, including overseeing the executive branch and voting on treaties. In practice, absolute power in Iran rests with its supreme leader, Ayatollah Ali Khamenei.
Friday's election was the first since the bloody crackdown on the 2022 nationwide protests that followed the death of Mahsa Amini in police custody.
Amini, 22, died on September 16, 2022, after her arrest by Iran's morality police for allegedly violating the country's strict headscarf law forcing women to cover their hair and entire bodies.
The protests quickly escalated into calls to overthrow Iran's clerical rulers. In the severe clampdown that followed, over 500 people were killed and nearly 20,000 arrested, according to human rights activists in Iran.
with Reuters