Secretary of State Antony J. Blinken met with China’s leader, Xi Jinping, in Beijing on Friday, as the two countries worked to hold together a fractious relationship despite disputes over the economy, national security and geopolitical frictions in East Asia, the Middle East and Ukraine.

Both China and the United States have said they were hoping for progress on a few smaller, pragmatic fronts, including improving communications between their militaries and easing travel between the countries. But they remain at a standstill on fundamental strategic issues, including trade policies and territorial conflicts in the South China Sea and over Taiwan.

And with other disputes looming, both sides acknowledged the danger of the relationship sliding into further conflict.

The Biden administration is deeply concerned that cheap Chinese exports are threatening U.S. jobs, and is worried about China’s support of Russia in the Ukrainian war. And China has accused the United States of working to encircle Chinese interests in the Pacific.

Still, in his opening remarks to Mr. Blinken, Mr. Xi struck a conciliatory note.

“China is happy to see a confident, open, prosperous and thriving United States. We hope the U.S. can also look at China’s development in a positive light,” Mr. Xi said, according to Chinese state media.

Earlier in the day, Mr. Blinken spent more than five hours with China’s foreign minister, Wang Yi, in meetings and at a working lunch at the Diaoyutai State Guesthouse in Beijing.