Monday's referendum on the new constitution is widely expected to pass, but turnout will be seen as a test of Saied's popularity after a year of increasingly tight one-man rule that has seen scant progress on tackling the North African country's economic woes.
Speaking after voting got underway, Saied told journalists Tunisians faced a "historic choice".
"Together we are founding a new republic based on genuine freedom, justice and national dignity," he said.
He also accused unnamed rivals of distributing money to persuade people not to vote, without giving evidence.
"We will not let Tunisia fall prey to those who are stalking it, from inside and out," he said.
The referendum comes a year to the day after Saied sacked the government and froze parliament in a power grab that his rivals condemned as a coup against the only democracy to have emerged from the 2011 Arab Spring uprisings.
His moves were however welcomed by many Tunisians tired of a grinding economic crisis and a system they felt had brought little improvement to their lives in the decade since the overthrow of dictator Zine El Abidine Ben Ali.
Critics, however, have condemned the new constitution as a power grab by President Saied, giving him expansive powers at the expense of Parliament and the Judiciary.