The province is home to 21 per cent of the estimated 8.3 million registered voters and is considered a stronghold for the MPLA, which is widely expected to win the election and extend its uninterrupted 33-year rule.
Outside Luanda voting generally proceeded normally and some polling stations closed on schedule at 6 p.m. (1700 GMT).
Earlier on Friday, Asaias Samakuva, Unita's leader, said after meeting the head of the electoral commission that "the system practically collapsed and we have to do something to recover the process".
Asked by a reporter if he had requested the commission hold a fresh election, Samakuva said: "Yes".
His criticism was echoed by Ngola Kabangu, the leader of the National Liberation Front of Angola (FNLA) opposition party, who told reporters the election had been "extremely flawed", though he stopped short of demanding a repeat.
Al Jazeera's Stefanie Dekker, reporting from Angola, said that while polling had been extended, it was unlikely there would be a re-run.
Earlier, voters and a European Union observer mission complained of disorganisation in the ballot.
Most Angolans appeared to revel in the opportunity to vote on Friday, the first time they have done so since the end of the country's bloody 27-year civil war in 2002 that killed 500,000 people.
But scores of polling stations failed to open on time, while others remained closed for several hours after voting began.
"People were very patient ... the organisers are the one's who've messed up here today," Dekker reported.
The ruling Popular Movement for the Liberation of Angola (MPLA) appears confident that Angolans will vote to extend its uninterrupted 33-year rule.
Unita hopes that discontent over the government's failure to address economic issues will boost its campaign.
Angola is Africa's second-largest oil exporter and economic growth is in double digits, but many people remain in poverty.
Two-thirds of Angolans live on less than $2-a-day and at least 40 per cent of the workforce is unemployed.
In an apparent admission of the government's failings to distribute oil wealth, Jose Eduardo dos Santos, the leader of the MPLA, pledged "change" at a final campaign rally on Thursday.
"For us, change does not necessarily come about by a change of party. To change public policies which haven't worked ... we must change the members of the team who are bad," he said.
In the election, the party hopes to boost its share of the 220-seat parliament, possibly winning a two-thirds majority that would allow it to amend the constitution.
The MPLA held 129 seats going into the election, with the remainder mostly controlled by Unita.
Friday's vote is the first attempt to hold a poll in Angola since failed elections in 1992 when Jonas Savimbi, the former Unita leader, withdrew from the second round of a presidential poll after accusing Dos Santos of rigging and civil war resumed.