The polls opened across the Indian Ocean archipelago at 8 a.m. (0500 GMT) for the 338,940 registered voters out of its 800,000 population. Voting ends at 6 p.m.
Comoros has experienced around 20 coups or attempted coups since winning independence from France in 1975 and is a major source of irregular migration to the nearby French island of Mayotte.
Some opposition leaders have called for a boycott, accusing the election commission of favoring the ruling party. The commission denies this, saying the process will be transparent.
"I am delighted with this anchoring of democracy in our country," Assoumani told reporters after voting in his home town of Mitsoudjé, adding that he hoped for victory in the first round.
The former army officer first came to power in a coup in 1999. He has since won three elections and has served as the chair of the African Union for the past year.
He won the 2019 election with 60% of the vote, breaching the 50% mark required to avoid a run-off. Critics say since then his government has cracked down on dissent, an accusation it denies.
Assoumani's opponents include a former interior minister and Salim Issa, a medical doctor and flagbearer for Juwa, former president Ahmed Abdallah Sambi's party.
"We welcome the conduct of the vote. We hope that everything will continue calmly," Issa wrote on social media from Foumbouni, his hometown in the south of the Comoros.
Sambi is now behind bars after being sentenced to life in prison in 2022 for high treason related to accusations of corruption. Political protests have been repeatedly banned for security reasons.
Comoros changed its constitution in June 2018 to remove a requirement that the presidency rotate among its three main islands every five years. This allowed Assoumani to seek re-election.
The opposition leaders calling for a boycott and their supporters have wanted the armed forces barred from involvement in the elections and the unconditional release of Sambi and other political prisoners.
Provisional results are expected on Friday, according to the election commission.