Anchor: The presidents of South Korea and the U.S. met ahead of the Asia-Pacific Economic Cooperation(APEC) summit in Gyeongju. During the meeting, President Lee Jae Myung promised to increase Seoul's defense spending to reduce the burden on Washington and requested that Washington relax its restrictions on Seoul's use of nuclear fuel, while U.S. President Donald Trump pledged to work towards holding talks with North Korea amid the current nuclear stalemate. 
Kim Bum-soo has more. 

Report: Ahead of the Asia-Pacific Economic Cooperation (APEC) summit, President Lee Jae Myung and U.S. President Donald Trump held a bilateral summit in Gyeongju Wednesday.

During the meeting that lasted for around an hour and a half, the two leaders sought ways to modernize their nations' alliance as the United States works to counter China's expanding presence in the Asia-Pacific region. 

[Sound bite: President Lee Jae Myung (Korean-English)]
"From now on, I believe the ROK-U.S. relationship must evolve into a modernized alliance, a future-oriented, comprehensive, strategic alliance. South Korea also intends to significantly enhance its own defense capabilities through increased defense spending and the development of its defense industry."

[Sound bite: US President Donald Trump]
"We're going to make ships together in the United States, and we're going to start up shipbuilding, and we'll be right at the top or, at least, for the top, in a pretty short period of time. But we have a lot of industries that are together, and we have a lot of industries where we're leading. 

Lee also asked Trump to allow South Korea to refine fuel to supply its own nuclear-powered submarines.

[Sound bite: President Lee Jae Myung (Korean-English)]
"Mr. President, I hope you will decide to ensure we get fuel for our nuclear-powered submarines. It's not that we intend to build submarines carrying nuclear weapons, but the limited diving capabilities of diesel-electric submarines limit our ability to track North Korean or Chinese submarines."

All eyes will be on Trump again on Thursday, when the U.S. leader is scheduled to hold a summit with Chinese President Xi Jinping, following a period of tension over China's expansion of its curbs on exports of rare earth minerals earlier this month.

Trump, however, noted that another surprise meeting with North Korean leader Kim Jong-un is unlikely this time around. 

[Sound bite: US President Donald Trump]
"I know Kim Jong-un very well. We get along very well. We really weren't able to work out timing. We have President Xi coming tomorrow. That was something that, obviously, is very important to the world, to all of us. You'll be watching very carefully. We're meeting right here. And we're all looking forward to that. I think it's going to work out very, very well for everybody."

Lee nevertheless praised Trump's willingness to meet with North Korean leader Kim Jong-un during the meeting, saying the U.S. president's peacemaking efforts will have the support of South Korea and its people. 

The South Korean leader said Seoul and Washington have been planting the seeds of a better future, creating opportunities to improve relations.
Kim Bum-soo, KBS World Radio News.