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Story highlights

NEW: Obama tells Chinese officials he's disappointed and concerned over Snowden

Deputy secretary of state: The United States has made its disappointment clear

Chinese official: Hong Kong handled the case "in accordance with the law"

Snowden has requested asylum in dozens of countries since he left Hong Kong

Washington CNN  — 

U.S. officials have told Chinese officials that they’re disappointed with the way China and Hong Kong handled the case of former NSA contractor Edward Snowden.

President Barack Obama expressed “disappointment and concern” over the matter during an Oval Office meeting with Chinese officials on Thursday, the White House said.

U.S. concerns were also made clear during two days of talks in Washington this week, U.S. Deputy Secretary of State Bill Burns told reporters.

“When we encounter differences and sensitive issues, we need to address them directly in consultation with one another,” Burns said. “And that is why we were very disappointed with how the authorities in Beijing and Hong Kong handled the Snowden case, which undermined our effort to build the trust needed to manage difficult issues.”

Snowden left Hong Kong on June 23 and flew to Moscow, where he is believed to be holed up inside Sheremetyevo International Airport.

At the time, Hong Kong officials had said a U.S. request for a provisional arrest warrant for Snowden “did not fully comply with the legal requirements under Hong Kong law” so it asked for additional information. Because Hong Kong didn’t have enough information, “there is no legal basis to restrict Mr. Snowden from leaving Hong Kong,” the government said.

Measured tones mask Washington’s fury with Hong Kong over Snowden

Chinese State Councilor Yang Jiechi defended the handling of the Snowden case Thursday. Responding to the U.S. criticism, he said, “the central government of China has always respected the Hong Kong SAR government’s handling of cases in accordance with law. The Hong Kong SAR government has handled the Snowden case in accordance with law and its approach is beyond reproach.”

Speculation over Snowden’s next steps

Since his arrival in Moscow, Snowden has requested asylum in dozens of countries, sparking a surge in speculation over his next steps.

WikiLeaks, which is aiding him in his bids for asylum, said in a Twitter post Wednesday that Snowden’s “flight of liberty” campaign was starting, promising further details. But details about where the former National Security Agency contractor is going – and how he’ll get there – have remained hard to come by.

Out of Russia: Snowden’s options

The presidents of Venezuela and Bolivia have said their countries would give Snowden asylum, and Nicaragua’s president said he would offer it “if circumstances permit.”

Snowden, who faces espionage charges in the United States, is slammed as a traitor by critics and hailed as a hero by supporters. He has admitted releasing classified documents to the media and argues that he did so to expose serious violations of the U.S. Constitution.

Feds start building case against NSA leaker

“I have watched and waited and tried to do my job in the most policy-driven way that I could, which is to wait and allow other people, leadership, to sort of correct the excesses of government if we go too far,” he said in an interview with the Guardian posted online this week. “But that’s not occurring and, in fact, we’re compounding the excesses of prior governments and making things more invasive, and no one is really standing to stop it.”

U.S. lawmakers have warned that any country that shelters Snowden could face economic sanctions.

A ‘new model’ for U.S.-China relations?

Last month U.S. President Barack Obama and Chinese President Xi Jinping met in a two-day summit California, pledging to build a “new model” of relations between the two nations.

On Thursday, Burns said that China’s handling of the Snowden case was not consistent “with the type of relationship, the new model that we both seek to build.”

But despite concerns over Snowden, the White House said Thursday that Obama had praised some developments in China.

“The president discussed the economic reforms underway in China and their compatibility with policies the administration is pursuing at home,” the White House said. “He also welcomed China’s important new commitment to open its economy to U.S. investment in a bilateral investment treaty that it is negotiating with the United States.”

CNN’s Catherine E. Shoichet contributed to this report.