U.S. Secretary of State John Kerry arrives for a press conference at the ASEAN meeting in the International Conference Center in Bandar Seri Begawan, Brunei, Monday, July 1, 2013. (Vincent Thian/AP)

BANDAR SERI BEGAWAN, Brunei — Secretary of State John F. Kerry praised China Monday for what he called “very firm statements and very firm steps” insisting that North Korea give up its nuclear weapons program, even as he said China could have done more to help the United States in apprehending fugitive leaker Edward Snowden.

Kerry arrived here Monday for two days of talks with his counterparts across Asia, part of the Obama administration’s efforts to bolster its standing and influence with the East.

With China, “we have a lot of issues that we’re dealing with right now. Issues of major maritime security . . . [and] major, major issues with respect to North Korea, [where] China is cooperating with us,” Kerry said at a news conference. “Life and international relationships are often complicated by the fact that you have many things you have to work on simultaneously.”

Chinese Foreign Minister Wang Yi, who met privately with Kerry Monday, told reporters that his government had urged North Korea to give up its nuclear weapons program, and called for early resumption of six-party talks, which include the United States, China, the two Koreas, Japan and Russia.

A senior State Department official said that China’s public backing for denuclearization of North Korea, as well as its “violent agreement” on the subject with Kerry in private, were major steps forward. The official spoke on condition of anonymity about the closed-door meeting.

Other tangible signs of Chinese cooperation, the official said, included the state visit to Beijing this month of South Korean President Park Geun-hye and the relative cold shoulder given there to a visiting senior North Korean official. China’s apparent policy shift comes after North Korea ignored appeals from Beijing and went ahead with a long-range rocket launch in December and its third nuclear test in February.

Kerry’s praise came even as he criticized the decision by authorities in Hong Kong to allow Snowden, a former National Security Agency contractor who leaked details of intelligence surveillance programs, to fly from Hong Kong to Moscow while the United States was asking for his extradition to face federal charges.

Kerry also discussed North Korea in a trilateral meeting with the foreign ministers of South Korea and Japan. Active participation in regional groups such as the 10-nation Association of Southeast Asian Nations, and an expanded group of Asian nations that will meet here Tuesday — including North Korea — is a major pillar of the “rebalance” of U.S. policy toward Asia.

Both meetings have also included extended talks on the South China Sea, where Kerry and his predecessor, Hillary Rodham Clinton, have strongly supported peaceful resolution of the long-standing dispute between China and Southeast Asian nations over maritime routes and resources.

The State Department official discounted an agreement made Sunday between ASEAN and China to meet in September to discuss proposals for a binding code of conduct for the sea, saying it was more interested in China’s behavior toward its neighbors than in talks about documents.

At his press conference, Kerry disputed a questioner who suggested he and the administration, despite claiming a policy “pivot” toward Asia, devoted most of their time and attention to the Middle East and Europe.