Margvelashvili urged Georgians on June 15 to "be active" in the elections, which he said "will demonstrate the victory of democracy in Georgia."
Mayoral offices in 12 cities and seats in 71 district and city councils in Georgia are at stake in the municipal polls in which 24 parties and blocs are represented.
The vote -- in which some 3.5 million voters are eligible to take part in -- are seen as the first test for the ruling Georgian Dream coalition government.
Prosecutors have launched probes into cases of alleged pressure on opposition candidates to withdraw from the elections.
The United States Embassy said last week it was "increasingly concerned" by such reports.
Georgia is due to sign an EU Association Agreement this month.