Algeria's President Abdelmadjid Tebboune posted online Thursday that "several children" had died. However, authorities have not disclosed the ages of the victims.
Polling stations, which opened at 8:00 am local time (0700 GMT) and closed at 8:00 pm, were nearly empty in the capital Algiers as of early afternoon, an AFP journalist reported.
Switzerland moved into the last 16 of the World Cup with a controlled 2-0 win against Algeria on Thursday.
Algeria and Austria played out an incredible 3-3 draw in Kansas City on Saturday that ensured both teams qualified for the World Cup knockout rounds and eliminated Iran.
Algeria came behind to beat Jordan 2-1 in a World Cup Group J game on Monday, eliminating the Asian debutants from the tournament.
Algeria is the first stop on an 11-day tour of four African nations, covering 18,000 kilometres and also taking in Cameroon, Angola and Equatorial Guinea from April 13 to 23.