Almost three hours after voting began, turnout was weak in several polling stations in the 14 governorates where the first round of the elections are being held over two consecutive days.
Electoral officials said they expected the momentum to pick up in the afternoon when people end their working day.
Some voters said they were enthusiastic about casting their ballots in the long-awaited election.
“I cared to vote today because I wanted to back the candidates who have no connection with the old regime,” a female voter said, as she left a polling station in the district of al-Haram in Giza near Cairo.
The 34-year-old housewife was referring to the former regime of longtime dictator Hosny Mubarak who was ousted in the 2011 uprising.
“I don’t think the people will vote again for the remnants of the Mubarak regime. Egyptians have learnt their lesson,” she told dpa.
Many contenders in the elections were former members of Mubarak’s now-defunct party.
But the largest numbers of the candidates are open backers of President Abdel-Fattah al-Sissi, who led the military’s overthrow of Morsi following street protests against the Islamist leader.
The Salafist al-Nour Party is the only Islamist force contesting the current elections.
Morsi’s Muslim Brotherhood is outlawed. Other Islamist parties have announced boycotting the polls, saying they are undemocratic.
“I was eager to come and vote in favour of al-Nour for it will be the only party that could help protect Islam in parliament,” a woman wearing a full-face veil said at a polling station in Giza, famed for the pyramids.
“If the al-Nour candidate in my constituency wins, I’m sure he will seek to apply God’s sharia (Islamic law),” the 40-year-old added.
Conservative women in Egypt usually do not divulge their names in public.
The reason for showing up at the same polling station was different for a 25-year-old man, who declined to give his name.
“I am here because I want to invalidate my vote,” he said.
“The coming parliament will not be different from the ones under Mubarak, who used to impose his will and pass the laws that appealed to him.”
Under a 2014 constitution, the parliament has vast powers including the right to impeach the president and call for early presidential elections.
However, the coming assembly with a five-year term is unlikely to pose a serious challenge to al-Sissi whose supporters among the candidates are expected to make big wins in the election.
On Saturday, al-Sissi called on Egyptians to vote in large numbers and elect the “best representatives” for the parliament.
The first hours of Sunday’s balloting went smoothly, according to Local Development Minister Ahmed Badr.
“Elections started as scheduled and are running without problems,” he told private TV station al-Hayat.
Some 430,000 security troops have been deployed outside polling stations, local media reported.
Egypt has seen a wave of deadly militant attacks since Morsi was deposed in July 2013 following massive street protests against his rule.
About 27.4 million Egyptians are eligible to vote in the first round of the election.
The number of seats up for grabs in the first round is 286, contested by 2,573 candidates including 112 women.
Polling stations are scheduled to close at 9 pm (1900 GMT).
The final results of this round are expected to be announced on October 30.
The two-round vote running through December is the third and last step in an army-backed transition plan announced following Morsi’s overthrow.
The two other steps were writing a new constitution and holding a presidential election.
The new parliament will be Egypt’s first in more than three years.
In 2012, the country’s top court dissolved the Islamist-led legislature, saying it had been elected on faulty rules.