Weah, 57, who turned to politics after a successful soccer career, says he needs more time to fulfill his promise to rebuild the West African nation's broken economy, institutions and infrastructure, pledging to pave more roads if reelected.
Elected in 2017 in the country's first democratic change of power in over 70 years, Weah is running against 19 other presidential candidates. To avoid a runoff, the winner must secure 50% of votes cast, plus at least one more vote.
Wrapping up his campaign after a parade across the capital Monrovia on Sunday evening, Weah cast his first term as a success despite significant challenges.
The iron-ore rich West African nation is still struggling to emerge from two devastating civil wars between 1989 and 2003, that killed over 250,000 people, and a 2013-16 Ebola epidemic that killed thousands.
"I'm proud of the record of achievement in a very difficult period. We were able to do much with less resources and solve many structural problems," Weah told cheering supporters.
He has faced criticism from the opposition and Liberia's international partners for not doing enough to tackle corruption during his first term in office. Last year, he fired his chief of staff and two other senior officials after the United States sanctioned them for corruption.
In his final speech, he highlighted other steps taken to address graft including the appointment of independent members to the Liberia Anti-Corruption Commission.
"In our second term, we plan to increase efforts on our war on corruption," he said.
Weah's main challenger is former Vice-President Joseph Boakai, 78, whom he defeated in a runoff in 2017. Boakai has campaigned on what he calls the need to rescue Liberia from alleged mismanagement by Weah's administration.
Voters will also select members of the 73-seat lower house, and half of the 30-member senate.
Although campaigning for the vote has been mostly peaceful, sporadic clashes have broken out between supporters of rival parties, prompting the United Nation's rights office to express concern about election-related violence after two people were killed in September.
On Sunday as campaigns closed in the capital, several people were wounded when fighting broke out between rival supporters.
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