WASHINGTON — President Obama gathered more than 50 world leaders here on Thursday to discuss one of his favorite topics: locking down nuclear weapons. But it was Mr. Obama’s meeting with one of the less friendly of those leaders, President Xi Jinping of China, that captured most of the attention.

The leaders announced that the United States and China would sign a climate change accord later in April, a show of unity on an issue that has become a bright spot in the tangled relationship between the two countries. But they quickly moved on to more contentious issues, with Mr. Obama pressing Mr. Xi on China’s construction of military facilities in the South China Sea, actions that a White House official said belied a pledge the Chinese president had made last fall not to militarize those waters.

“Like China and other countries, the United States has significant interests in the Asia-Pacific region,” Mr. Obama said to Mr. Xi before the meeting, his only extended encounter with a visiting leader at the Nuclear Security Summit, which will conclude on Friday.

“Our two countries have some disputes and disagreements,” Mr. Xi replied. He called for both sides to “avoid misunderstanding and misperceptions,” and to respect each other’s core interests — a polite warning not to meddle in the South China Sea, which Beijing regards as a core interest.