The Supreme Council of the Armed Forces said turnout could go as high as 80 percent after elections were extended an additional day, al-Masry al-Youm reported.
There were no reports of attacks on polling places or stolen ballot boxes as the second scheduled day of voting began Tuesday, The New York Times reported.
However, some civil society groups complained international observers did not have a clear role in the process.
Unexpectedly large crowds of Egyptians turned out to vote for the first time since the ouster of President Hosni Mubarak in February.
Egypt's Interior Ministry apologized for procedural mistakes reported during the first round of the People's Assembly elections held in nine governorates, including Cairo, Egypt's al-Masry al-Youm said.
Several polling stations experienced delays, as long as 3 hours in some cases, due to the late delivery of ballots.
"Pardon us for the mistakes. It's a totally new experience for all Egyptians," said an apology issued by the Interior Ministry.
Egypt's High Elections Commission said it suspended voting at one polling station after discovering a policeman was marking the name of a specific candidate on ballots.