Singapore's prime minister has urged the US to maintain ties with both China and Japan because south-east Asian nations do not want to "choose sides".
Mr Bush agreed to attend the ASEAN summit in September
Lee Hsien Loong told President George W Bush the two countries have a major impact on the region's prosperity, after bilateral talks in Washington.
He also encouraged the US to strengthen ties with members of the Association of South-East Asian Nations (Asean).
Mr Bush responded by agreeing to attend the organisation's summit in September.
The president will stop in Singapore for his first visit to the 10-nation meeting on his way to the Asia-Pacific Economic Co-operation (APEC) forum in Sydney.
"I talked to Prime Minister Lee about America's desire to stay in close contact with not only Singapore, but our partners in what we call the Asean nations," Mr Bush said.
"To this end, the prime minister has invited me, and I've accepted, an invitation to go back to Singapore to talk to our partners and friends about trade and security, and we'll do so on my way to the APEC meetings in Australia."
'Friends with both'
Mr Lee welcomed Mr Bush's acceptance of his invitation, but warned him not to try to push Southeast Asia into choosing between the region's two dominant powers.
"We discussed America's relations in Asia, with China, with Japan, and Korea," he said.
"Those two are important to south-east Asia because they set the context within which south-east Asia can prosper."
"Good relations between America and the major countries... are critical because the south-east Asian countries want to be friends with both, and do not want to have to choose sides with either."
Singapore's prime minister also warned Mr Bush that it was vital that his administration worked to bring about peace between Israel and the Palestinians.
"It affects America's standing in Asia and the world, and also the security environment in Asia because extremists, the jihadists, watch carefully what's happening in the Middle East and take heart, or lose heart, depending on what's happening," Mr Lee explained.