President Surangel Whipps Jr is contesting the post against his brother-in-law, former president Tommy Remengesau, who stood at traffic intersections on Monday directly appealing to drivers for support.
Voters will also elect 13 members of the national senate.
Palau this year renewed a Compact of Free Association with Washington, in a deal that will see it receive $US890 million ($A1.3 billion) in economic assistance over 20 years in return for allowing continued US military access to its maritime zone, air space and land.
Palau's population of 18,000 is spread across an archipelago that sits between the Philippines and the US military base on Guam. The US military is constructing an over-the-horizon radar on Palau, scheduled to be completed in 2026.
Tommy Remengesau has warned about "foreign influences" overshadowing Palau's independence. (Mick Tsikas/AAP PHOTOS)
Palau is one of only 12 countries that have diplomatic ties with Taiwan, and Whipps has said China's move to bar tourist groups from travelling to Palau, and a cyber attack in March, are examples of pressure from Beijing to switch ties.
To counter the fall in Chinese tourist arrivals, Palau has opened direct flights to Japan and Australia, with support from those governments.
Tax reform has emerged as an election issue, with Remengesau's campaign arguing big business is not paying enough, and pledging tax incentives for small business.
The Palau Media Council, in a statement, said it was concerned by a lawsuit filed against the Island Times newspaper by Surangel and Sons Co, a retail and construction company owned by Whipps' father, after the newspaper reported allegations circulated on social media about the company's tax payments.
The defamation lawsuit alleges the newspaper did not verify the social media claims, which were false, and designed to sway voters, the president's father said in several statements.
Whipps' request for the US to install a permanent Patriot missile shield has stalled, after Palau's Senate passed a resolution rejecting it.
During the election campaign, Remengesau said Palau needs to "ensure that foreign influences do not overshadow our identity or compromise our independence".
His campaign did not respond to questions on which foreign influence he was referring to.
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