U.S. State of Secretary Rex Tillerson, left, chats with China's President Xi Jinping at the Great Hall of the People in Beijing. (Lintao Zhang/Pool Photo via AP) (Lintao Zhang/AP)

While his boss was goading China over Twitter, new Secretary of State Rex Tillerson has been trying to build a constructive and “results-oriented” relationship with the leadership in Beijing.

And though his warnings about the possibility of eventual military action over North Korea have raised hackles here, Tillerson received a warm welcome from China’s president on Sunday.

“You have made a lot of active efforts to achieve a smooth transition in our relationship under the new era,” President Xi Jinping told Tillerson as the men sat down for talks in the Great Hall of the People. “And I also appreciate your comment that the China-U.S. relationship can only be defined by cooperation and friendship.”

But some critics say Tillerson has bent too far, handing Beijing what Chinese news media reports are calling a “diplomatic victory.”

After meeting China’s Foreign Minister Wang Yi on Saturday, Tillerson voiced Chinese catchphrases about the relationship, including the avoidance of conflict and confrontation and the need to build “mutual respect” and strive for “win-win” cooperation.

The phrase “mutual respect” is key: In Beijing, that is taken to mean each side should respect the other’s “core interests.”

In other words: The United States should stay away from issues such as Taiwan, Tibet and Hong Kong — and in principle almost anything China’s Communist Party deems a vital national security concern. Increasingly, that also appears to include China’s territorial claims in the contested waters of the South China Sea.

Several Chinese foreign policy experts called the comments “very positive” and in line with a concept Beijing has long advocated — what it calls “a new model of great power relationships,” which would put the two nations on a roughly equal footing.

Jin Canrong, a Sino-U.S. relations expert at Renmin University of China in Beijing, said Tillerson’s comments came as a surprise.

“China has long been advocating this, but the United States has been reluctant to accept the point of ‘mutual respect,’ ” Jin said. “Tillerson’s comment will be very warmly welcomed by China.”

But Bonnie Glaser, senior adviser for Asia at the Center for Strategic and International Studies, said the United States should use its own language to describe bilateral relations, not embrace China’s.

More important, “mutual respect” signals acceptance of “a litany of issues that China views as nonnegotiable,” she said. “By agreeing to this, the U.S. is in effect saying that it accepts that China has no room to compromise on these issues.”

That would be a mistake, said Glaser, adding that China has shown no inclination to accept what might be seen as U.S. “core interests,” such as its alliances in Asia.

On the campaign trail last year, candidate Donald Trump pilloried China as a security threat and, particularly, a stealer of American jobs. On Friday, as Tillerson prepared to make his way to Beijing on the third leg of his Asian tour, Trump took to Twitter to criticize China for not helping rein in North Korea’s nuclear program.

Tillerson has almost certainly been pushing China hard on the North Korean issue behind closed doors. But in public, his tone has been much more measured, judging this to be a better way to save China’s face and gain its cooperation.

He could have received assurances from China — for example, over North Korea or trade — that he felt merited giving ground in return. Or perhaps the former ExxonMobil boss is simply not that worried about parsing diplomatic language and is more focused on results.

“Tillerson’s remarks were probably an effort to provide Xi face in public, while behind doors, the conversation was probably more direct,” said Walter Lohman, director of the Asian Studies Center at the Heritage Foundation. “At least I hope so. Because, assuming Xi paraphrased Tillerson accurately, it is certainly not true that ‘the China-U.S. relationship can only be defined by cooperation and friendship.’ ”

Ironically, the Obama administration also ran into criticism for using the phrase “new model of relations” in 2013 and 2014, before backing away from wording that was seen as uncomfortably close to the Chinese formulation.

Ely Ratner, who worked as Vice President Joseph R. Biden’s deputy national security adviser and is now a senior fellow at the Council on Foreign Relations, took to Twitter to call it a “big mistake and missed opportunity” for parroting Chinese government “platitudes and propaganda.”

“China’s characterization of the U.S.-China relationship, as exemplified by those phrases, portends U.S. decline and accommodation,” he wrote in an email. “Tillerson using these phrases buys into this dangerous narrative, which will only encourage Chinese assertiveness and raise doubts in the region about the future of U.S. commitment and leadership in Asia.”

As for Trump, he had shown so little regard for Beijing’s sensitivities that he even questioned whether the United States should continue to uphold the one-China policy, which rules out independence and diplomatic recognition for Taiwan.

That had spooked and angered Beijing until Trump backed down during what has been described as a warm and cordial telephone conversation with Xi last month.

On Sunday, China’s president said that, after talking, both leaders “believe that we can make sure the relationship will move ahead in a constructive fashion in the new era.”

Both sides are talking about a face-to-face meeting between the leaders. China realizes that a personal rapport with Trump is important and watched in consternation as Japan’s Prime Minister Shinzo Abe made an early visit to Trump’s Mar-a-Lago resort in Florida.

Tillerson seemed to acknowledge that getting his president better acquainted with China would make his job easier.

The “very lengthy” phone call between the leaders not only improved China’s understanding of the United States but also Trump’s understanding of China, Tillerson said. “And he looks forward to enhancing that understanding in the opportunity for a visit in the future.”

“We know that through further dialogue we will achieve a greater understanding that will lead to a strengthening of the ties between China and the United States and set the tone for our future relationship of cooperation,” he said.

Tillerson and Xi nodded as the other spoke, both flanked by officials and aides in the lavishly decorated Fujian Room in the Great Hall of the People, on the west side of Beijing’sTiananmen Square, before the news media was ushered out for Tillerson’s last meeting of his three-nation Asian tour.

Even more than trade ties, North Korea has emerged as the biggest thorn in the relationship between Washington and Beijing. The United States wants firmer action to isolate Pyongyang and persuade the regime to abandon its nuclear program.

Tillerson says diplomatic efforts have failed and has not ruled out eventual military action. China, though, opposes anything that could bring down the regime in Pyongyang and bring instability to its borders.

It insists that dialogue is the only way forward, and Wang, the foreign minister, told Tillerson on Saturday that the United States should remain “coolheaded.”

Yet North Korea upped the ante even further Sunday by announcing it had carried out a rocket engine test “of historic significance.”

Luna Lin contributed to this report.