The Senate Council, parliament’s upper house, was reinstated as part of constitutional amendments adopted in 2019.
Egypt used to have the Shura Council, another name for the upper house, until 2013 before it was dissolved in the 2014 constitution.
The constitutional changes also allowed Egyptian President Abdel-Fattah al-Sisi, who first took the office in 2014, to stay longer in power, possibly until 2030.
The Senate would be formed of 300 members, two thirds of them elected by public vote and the remaining third appointed by the president.
A vote was held on Sunday and Monday for Egyptian expatriates.
The initial results of the vote will be announced on Aug. 19, with a run-off scheduled on Sept. 6 to Sept. 7 for expatriates and Sept. 8 to Sept. 9 in Egypt.
All the polling stations would be sterilised before the start of voting, and voters would be required to wear masks and observe social distancing while casting their ballots.
Public gatherings for campaigning had been banned.
Lashin Ibrahim, head of the elections authority, has called on Egyptians to heavily participate in the vote.