Rafael Correa is sure that his popularity will help his allies win the election of an assembly rewriting the nation's constitution.
Correa's opponents accuse him of seeking to concentrate power and note he proposes letting presidents serve two consecutive four-year terms instead of the one allowed now. Correa denies he plans to maintain himself in power indefinitely.
Correa's push for a new charter follows in the footsteps of socialist leaders Hugo Chavez in Venezuela and Evo Morales in Bolivia.
Pre-election polls showed Ecuadoreans, disillusioned with their political system, were likely to give the president's new political movement the greatest number of seats in the 130-member body.
"There are going to be profound changes in our country for the good of everyone," Correa predicted as voting stations opened.
If Correa's backers fall short of an outright majority, he could try to form alliances that would let him push through his reforms.
An official tally of results was expected to take up to a month because of the complexity of the ballot. More than 3,200 candidates were vying for seats in the assembly.
Voting was peaceful in most of the country, but angry voters in Esmeraldas province on Ecuador's coast burned two ballot boxes, forcing suspension of voting there, officials said.
Correa, 44, a former economy minister and an ally of Venezuelan President Hugo Chavez, says the assembly is necessary to eliminate the power of traditional political parties, which he blames for the country's instability and corruption.
An overwhelming 82 percent voted in April to create the assembly, which will have the power to dismiss any elected official as well as write a new constitution.
Correa, who took office in January, says the assembly will pave the way for socialism.
He has not detailed his reforms, but Correa is expected to call for the closing Congress and replacing it with a parliamentary commission until a legislature is elected under a new charter.
Correa's foes say the president is simply power-hungry.
"Every leader who yearns for absolute power disguises it or hides his intentions with a savior's message, with a populist message to attract support," said Blasco Penaherrera, a former vice president and assembly candidate for the right-wing Social Christian Party.
The import of liquefied natural gas from the United States will not grow, even if Germany exits the Nord Stream-2 project, German Minister of Economy and Energy Peter Altmeier said