The South Korean parliamentary speaker and key officials from the major political parties were among early voters.
Duterte made the announcement following the recent visit of three Chinese warships to Davao City.
The North Korean state media reports that Pyongyang has threatened to attack the Carl Vinson.
An ASEAN diplomat says the statement discussed was a genuine representation of the atmosphere of the Manila meetings.
Trump told a Pennsylvania crowd he was just getting started on meeting his campaign promises.
The negotiation started as early as 2001 when the Philippine government initiated the peace talks and invited the Malaysian government to serve as a third party facilitator.
The 71-year-old leader says he would not raise the tribunal ruling during the ASEAN events this week.
Among those recently killed last week was Commander Muamar Askali also known as Commander Marwan, an Abu Sayyaf sub-leader known for his maritime piracy and kidnapping.
The United States and North Korea have been stepping up warnings to each other in recent weeks over North Korea's development of nuclear weapons.
Moon Jae-in, the presidential candidate of the Democratic Party of Korea, denounces the move of Thaad deployment.
On Monday, Donald Trump called for tougher new UN sanctions on Pyongyang, saying the North was a global threat and "a problem that we have to finally solve".
South Korean Defence Ministry spokesman Moon Sang Gyun says Seoul is holding discussions with the US Navy.
North Korea is on a quest to develop a long-range missiles that will be capable of hitting the US mainland with a nuclear warhead.
Analysts say Pence's Muslim outreach in Indonesia will likely not be enough to assuage fears that the Trump administration is anti-Islam.
The national elections commission will announce official results in early May.