CAIRO — The message blared from social media videos, from banners too big to miss, and from the upbeat Election Day songs playing so boisterously on jumbo speakers that they drowned out the nonstop honking of Cairo traffic: “Do the right thing. Vote.”

On many of banners, a green checkmark next to President Abdel Fattah el-Sisi’s image demonstrated the proper way to vote. But even if not all of the messaging was explicit, it was clear enough what doing the “right thing” meant: Voting “yes.”

Saturday was the first of three days of voting in an Egyptian referendum on a series of constitutional amendments that, if passed as expected, will effectively extend Mr. el-Sisi’s hold on power eight years beyond his current term, until 2030.

They will also expand Mr. el-Sisi’s authority, along with the military’s, at the expense of the judiciary and legislature, placing top judicial officials under his control and allowing him to appoint some members of a new legislative chamber.