The gathering aims to grapple with challenges such as climate change, drug crime and the Chinese test-firing of a ballistic missile in July that landed in the Pacific Ocean.
But at least five leaders won't attend, sending lower-ranked ministers in their place.
The 18-member Pacific Islands Forum is being hosted by Palau, a diplomatic ally of Taiwan.
Beijing claims the self-ruled island as part of its territory, and has protested against Taiwan's inclusion among aid partners invited to attend, which include China, Singapore, Japan, Britain and the United States.
Chinese diplomats had warned Pacific leaders not to appear at side events in Palau where Taiwan's foreign minister may be present, AFP was told.
"Our partners are welcome to sail with us but they do not choose our destination," Palau's President Surangel Whipps said at the opening ceremony, urging Pacific unity.
Solomon Islands Foreign Minister Rick Houenipwela said "strategic competition has sharpened around us".
"The forum must remain the political home where Pacific leaders speak honestly, listen carefully and decide our own thoughts," he said.
"Our partners are welcome and their support is valued, but this should help us realise our missions, not define them," he added.
Houenipwela spoke at the ceremony in place of his country's prime minister, Matthew Wale, who rushed home a day earlier to fend off a surprise push to unseat his government.
Wale had sought to reduce the Solomons' reliance on China after taking office in May, visiting Canberra, Washington and Tokyo to seek investment and vowing to review a secret security pact with Beijing.
Other leaders not attending include Kiribati's president and the prime ministers of Samoa and Vanuatu.
The head of government of the French territory of New Caledonia will also skip the summit, a forum official told journalists.
Fiji's delegation to Palau was led by the foreign minister, but it was not known whether the prime minister might join at a later stage.
- 'Lowers the expectations' -
The leaders' absence may weaken any joint Pacific statement on the Chinese missile test, said Oliver Nobetau, Pacific analyst at the Lowy Institute, a Sydney-based think tank.
"Not having these leaders there really lowers the expectation of whether or not we will see a strong statement come out of the Pacific Islands Forum," he told AFP.
Some Pacific leaders were staying at home to tackle domestic political priorities, said Nobetau, director of the institute's Pacific Islands programme.
Australia's Foreign Minister Penny Wong said Pacific countries "make their own decisions about their delegation and who leads them".
"This forum matters," she told the Australian Broadcasting Corporation.
"It enables decisions to be made for the Pacific by the Pacific and in a time of regional contest and competition... having a strong regional organisation and regional decision-making is one of the ways in which that asymmetry of power between great powers and smaller powers can be navigated."
Around 110 police officers drawn from various Pacific islands will provide security at the forum, the first large-scale demonstration of Pacific-wide cooperation on policing.
Australia, the biggest forum member and aid donor, has led efforts for the Pacific to provide its own security, arguing there is no need for China to have police in Kiribati and the Solomons.
"Investing in the security and prosperity of our Pacific neighbours makes our region safer and our economy stronger," Prime Minister Anthony Albanese said in a statement.
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