The Chinese state news media, in its readout of the call, said Mr. Trump had “stressed that he fully understood the great importance for the U.S. government to respect the One China policy,” and that “the U.S. government adheres to the One China policy.”

It also said the two leaders had agreed on the “necessity and urgency of strengthening cooperation between China and the United States” and noted that Beijing wants to work with Washington on a range of issues, including the economy and trade, science, energy, communications and global stability.

The timing of the conversation was significant, as Mr. Trump is about to welcome Japan’s prime minister, Shinzo Abe, for an extravagant three-day visit that will include a weekend of golf in Florida — a visit that will be closely monitored in China.

Among the issues Mr. Trump is expected to discuss with Mr. Abe, is the president’s commitment to a mutual defense treaty with Japan, which surfaced during the campaign. At the time, Mr. Trump said he was prepared to pull back from the pact unless Tokyo did more to reimburse the United States for defending Japanese territory.

On Thursday, Secretary of State Rex W. Tillerson met with officials at the White House to discuss issuing a statement about relations with China. His involvement was noteworthy because he had pledged, in written answers to questions after his Senate confirmation hearing, to uphold the One China policy.

Mr. Tillerson specifically rejected the idea, advanced by Mr. Trump, that Taiwan be used as a bargaining chip in a broader negotiation with China on trade, security and other issues.

On Wednesday, the White House sent a letter from Mr. Trump to Mr. Xi wishing him a happy Chinese New Year, which administration officials described as an effort to keep the relationship from unraveling further while they sought to resolve the tensions.

Relations between Washington and Beijing had been frozen since December, when Mr. Trump took a congratulatory phone call from Taiwan’s president, Tsai Ing-wen. The United States has not had diplomatic relations with Taiwan since 1979, and Mr. Trump defended the call by saying he did not know why the United States should be bound by the One China policy.

To lay the groundwork for a better relationship, Mr. Trump’s national security adviser, Michael T. Flynn, spoke last Friday with China’s top foreign policy official, Yang Jiechi. That call produced only a vague commitment to “reinforce high-level exchanges,” suggesting that Mr. Trump’s statements on China sill precluded a direct leader-to-leader exchange.

As a gesture of conciliation, Mr. Flynn and his deputy, K. T. McFarland, hand-delivered Mr. Trump’s letter to China’s ambassador to the United States, Cui Tiankai. Mr. Trump wrote that he wished “the Chinese people a happy Lantern Festival and prosperous Year of the Rooster.” He also said he “looks forward to working with President Xi to develop a constructive relationship that benefits both the United States and China.”

“This letter means they’re looking for creative ways to stabilize this relationship when Trump and Xi can’t talk due to differences over Taiwan policy,” said Evan S. Medeiros, who was senior director for Asia on the National Security Council under President Barack Obama.

But there were indications that the administration recognized it needed to do more. Mr. Tillerson, officials said, suggested that Mr. Trump publicly reaffirm his commitment to the One China policy as a way of breaking the deadlock and getting the two presidents back on the phone.

For Mr. Trump, it was a significant reversal. In an interview with Fox News in December, he said the policy should be contingent on extracting concessions from Beijing.

“We’re being hurt very badly by China with devaluation; with taxing us heavy at the borders when we don’t tax them; with building a massive fortress in the middle of the South China Sea, which they shouldn’t be doing; and, frankly, with not helping us at all with North Korea,” he said.

Since his inauguration, Mr. Trump has spoken by phone with about 20 foreign leaders. Although these are usually highly scripted affairs, Mr. Trump’s have been anything but. His conversation last week with Prime Minister Malcolm Turnbull of Australia turned contentious when Mr. Turnbull urged Mr. Trump to honor an agreement made under Mr. Obama to accept 1,250 refugees from an offshore detention center.

But arguably, no bilateral relationship is more important than the one between Beijing and Washington, and the fact that Mr. Trump and Mr. Xi had not talked since Mr. Trump took office in January has drawn increasing scrutiny.

“The U.S.-China relationship only works if the two leaders have a serious relationship and use their contact to do real business,” Mr. Medeiros said. “Given the rigidity of the Chinese system, leader-level contact provides essential stability, direction and momentum to U.S.-China ties.”

Administration officials are also keenly aware that the Chinese will be closely watching the visit of Mr. Abe, which begins here Friday with an Oval Office meeting, a White House lunch and a joint news conference. Then Mr. Trump will take Mr. Abe to Palm Beach, Fla., on Air Force One. The leaders plan to play golf at Mr. Trump’s club, Mar-a-Lago, and then they and their wives will have dinner there.

To the status-conscious Chinese, this red-carpet treatment will not go unnoticed. Analysts say it may reinforce their suspicion that the Trump administration is making Japan the centerpiece of its Asia strategy.

In Beijing, Lu Kang, a spokesman for China’s Foreign Ministry, expressed thanks for Mr. Trump’s letter. He dismissed as “senseless” speculation the idea that Mr. Trump had been snubbing Mr. Xi by not scheduling a phone call earlier. “The two countries share wide common interests, and cooperation is the only correct path for both,” Mr. Lu told reporters on Thursday.

Even before the phone call, Mr. Trump and his advisers had markedly shifted their tone toward China since the inauguration.

During the campaign, Mr. Trump advocated a 45 percent tariff on Chinese exports to the United States, complaining that China manipulated the value of its currency. This month, however, Ivanka Trump, the president’s daughter, attended a Lunar New Year celebration at the Chinese Embassy in Washington. Her daughter, Arabella, sang a New Year’s greeting in Mandarin that was widely viewed in China.

Ms. Trump’s husband, Jared Kushner, who is a senior adviser to Mr. Trump, met with Mr. Cui before the embassy event, part of a blossoming dialogue between the two men.

The business relationships between some of Mr. Trump’s advisers and leading Chinese companies with close links to the Communist Party may also be strengthening ties. Mr. Kushner took part in talks last year with the Chinese billionaire Wu Xiaohui to help redevelop the Kushner family’s crown jewel, a commercial building on Fifth Avenue.

“It’s an expression of good will,” Jia Qingguo, dean of the School of International Studies at Peking University, said of Mr. Trump’s letter. “It’s necessary to handle this relationship with practical cooperation.”