SEOUL, May 29 (Reuters) - South Korean President Yoon Suk Yeol begins the country's first summit with leaders of Pacific islands on Monday, as Seoul seeks to increase its influence in a region that has become the focus of intense geopolitical rivalry.

Yoon launched his administration's Indo-Pacific strategy last year, pledging to foster a "free, peaceful and prosperous" region built on a rules-based order, amid concerns over China's security ambitions for the strategic waters and economic leverage among the small island states.

The South Korean president held bilateral talks with some of the visiting Pacific leaders over the weekend including Kiribati President Taneti Maamau and Papua New Guinean Prime Minister James Marape.

"The president discussed expanding reciprocal cooperation in development, marine and fisheries as well as building health infrastructure and responding to climate change in bilateral meetings with each of the Pacific islands," Yoon's office said in a statement on Sunday.

South Korea's Indo-Pacific strategy also sees greater scope for trilateral cooperation with the United States and Australia to tackle regional challenges such as supply chains, critical minerals and climate change.

Still, while the Yoon government’s strategy indicates closer alignment with the U.S, "South Korea must still move cautiously between the two great power rivals given Seoul’s larger economic and geopolitical stakes in China relative to other U.S. allies,” said Andrew Yeo, a Senior Fellow at U.S. think tank Brookings Institution.

Australian Defence Minister Richard Marles will also attend the Korea-Pacific Islands Summit, his office said on Saturday, adding it would show cooperation between the 18 members of the Pacific Island Forum and South Korea for a secure region.

Australia and New Zealand are the largest members of the forum, a bloc of mostly small island countries at risk from rising sea levels caused by climate change and reliant on aid from development partners.

The bloc has taken a collective approach to dealing with major powers.

Indian Prime Minister Narendra Modi pledged more trade and development assistance in a summit with a dozen Pacific island leaders in Papua New Guinea (PNG) last week. The United States Secretary of State Antony Blinken also signed a defence agreement with PNG after a Pacific summit.

Micronesia could not attend the meeting in Seoul due to a typhoon, Yoon's office said.