Polling stations opened in a third of the country’s 27 provinces at 8:00 am (0600 GMT) on Wednesday.
The run-off in the second round of legislative polls, which takes place over two days, will see the two largest Islamic parties go head to head for 59 seats of the lower house.
The three-stage elections are the first since the ouster of former dictator Hosni Mubarak in February.
About 19 million people are eligible to cast their ballots in the run-offs, based on a mixed electoral system of party lists and individual candidacy.
Meanwhile, the clashes between the protesters and the security forces have left at least 14 people dead and over 500 others wounded in five days.
On Tuesday, thousands of Egyptians, mainly women, marched through the streets of central Cairo to protest the violence against people.
Egyptians have recently staged mass demonstrations against the continued rule of the Supreme Council of Armed Forces (SCAF) in recent weeks.
Protesters have been calling on the SCAF to hand over power to a civilian authority, accusing it of moving against the country’s popular revolution by using violence against civilians.
The SCAF took over after the ouster of Mubarak in a popular revolution in February.
Thousands of Egyptian women have poured on to the streets in the capital city of Cairo to protest the security forces’ brutal crackdown on female demonstrators.
The protest took place in the landmark Liberation (Tahrir) Square on Tuesday, days after army soldiers harshly beat a woman and ripped off her clothing while dragging her along the ground during a demonstration in the square.
Released footage and images of the half-naked female protester has sparked outrage among Egyptians.
“Our honor is a red line,” the women demonstrators shouted while gathering in the square, which has been the site of deadly clashes between Egyptian military forces and protesters since Friday.
“They know that people who don’t care about their own lives they care about their mother, wife and sister. So they wanted to humiliate the whole Egyptian people by humiliating women because they know it’s very sensitive,” said a demonstrator, referring to the humiliating conduct of security forces toward female protesters.
They also chanted slogans against the Head of the Supreme Council of the Armed Forces (SCAF), Field Marshall Hussein Tantawi, calling him a traitor.
“[The ruling generals] have to go, they are traitors,” the protesters said.
The Egyptian military’s violence against protesters in the past five days has left at least 14 people dead and hundreds more injured, according to the country’s health ministry.
The demonstrators call on the junta to immediately transfer power to a civilian government nearly one year after the country’s revolution toppled former dictator Hosni Mubarak