But Mr. Trump acknowledged recently that those efforts had failed. As a result, he has sharply escalated pressure on Mr. Xi to do more to punish the North.
The Trump administration last week imposed sanctions on a Chinese bank, accusing it of acting as a conduit for illicit North Korean financial activity. And Washington has taken a series of additional steps recently seen as affronts to Beijing, including accusing the Chinese government of human rights violations and selling $1.4 billion in weapons to Taiwan, which China regards as its territory.
In the latest sign of tension, an American naval destroyer on Sunday sailed near disputed territory claimed by Beijing in the South China Sea, prompting a furious response from the Chinese government.
Mr. Trump also raised trade issues with Mr. Xi, the White House said, a sign that he may become more vocal on economic matters as he seeks concessions from China on North Korea.
During the call on Monday, Mr. Xi said the relationship between the two countries had shown progress but was also affected by ânegative factors,â according to Xinhua, the state-run news agency. He urged the United States to handle Taiwan in accordance with the âOne Chinaâ policy. Under that policy, which has been in place since 1972, the United States recognized a single Chinese government in Beijing and severed its diplomatic ties with Taiwan.
In response, Mr. Trump reiterated his pledge to uphold the One China policy, Xinhua reported.
Cheng Xiaohe, an associate professor of international relations at Renmin University in Beijing, said that given the recent actions by Mr. Trump, it was âa little bit oddâ that Mr. Xi had agreed to the phone call.
Still, he said, the gesture seemed to indicate that China was seeking to maintain âstability and some momentumâ with Mr. Trump and perhaps deter him from resorting to more extreme measures, such as a military response.
âThe actions the administration has taken have upset the Chinese, no doubt about it,â Professor Cheng said. âThe conversations demonstrate that China is still willing to talk with Trump and work with the U.S. government to deal with North Koreaâs nuclear issues.â
Ruan Zongze, a former Chinese diplomat, said Mr. Trump was misguided in thinking that the situation in North Korea could be resolved by putting pressure on China.
âThe essence of the North Korea nuclear crisis is the adversarial relationship between the U.S. and North Korea,â said Mr. Ruan, who is executive vice president of the China Institute of International Studies, a government think tank. âYou canât say China should be the one to solve the North Korea crisis.â
Increasingly, Mr. Trump is also looking to other Asian nations, including Japan and South Korea, for help in resolving the crisis.
Kyodo News, a Japanese news agency, reported that Mr. Abe had praised the Trump administrationâs decision to impose sanctions on Chinese entities accused of conducting illicit business with the North. The agency said that Mr. Trump and Mr. Abe agreed to hold trilateral talks on North Korea with South Koreaâs newly elected president, Moon Jae-in, on the sidelines of the G-20 meeting in Hamburg.
Mr. Trump met Mr. Moon at the White House on Friday. Mr. Moon has urged dialogue with the North â an idea that Mr. Trumpâs advisers have shown little interest in.
Amid the tensions, North Korea has continued to stridently defend its weapons program. On Monday, the North reiterated that its missiles âcan hit any target in a speedy and accurate manner,â according to Yonhap, a South Korean news agency.