Notably absent from this week's meetings is US President Donald Trump, who has said several existing multilateral trade deals are unfair, and has railed against China over intellectual property theft, entry barriers to US businesses and a gaping trade deficit.
The 33rd summit of the Association of Southeast Asian Nations (ASEAN) will be chaired by Singaporean Prime Minister Lee Hsien Loong and will mark the ending of Singapore's chairmanship in the organization.
Both Singapore and China are expected to rally support for the Regional Comprehensive Economic Partnership (RCEP) pact now being negotiated, which is showcased to be a free trade deal that will encompass more than a third of the world's GDP.
The pact - which is less ambitious than the TPP in areas such as employment and environmental protection - groups the 10 ASEAN members plus China, India, Japan, South Korea, Australia and New Zealand.
Trump has demanded trade agreements that are fair and enforceable and based on the principle of reciprocity.
With the United States having pulled out of rival pact the Trans-Pacific Partnership (TPP), the RCEP is now the world's biggest trade deal. He did not directly refer to China's bruising trade war with the United States.More news: Trump blames 'poor forest management' for California fires
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However, Li is expected to appeal in Singapore for the need for the world's two largest economies to work together to resolve trade disputes, reiterating commitment made by Beijing's top leaders last week for market opening and lowering tariffs.
Leaders including Chinese Premier Li Keqiang and US Vice President Mike Pence are meeting this week in the city-state against the backdrop of a months-long trade dispute between Beijing and Washington.
Singapore is the first leg of Moon's six-day trip that will also take him to Papua New Guinea on Saturday and Sunday for this year's summit of the Asia Pacific Economic Cooperation forum involving Pacific Rim nations.
On the sidelines of the ASEAN and APEC summits, Moon also plans to hold a series of one-on-one meetings with other world leaders, including Russian President Vladimir Putin and Australian Prime Minister Scott Morrison.
The visit is part of Dr Mahathir's high-level introductory visits to Asean countries after being sworn in as the 7th Prime Minister of Malaysia in May.