By Humeyra Pamuk and Michael Martina

NEW YORK (Reuters) -U.S. Secretary of State Antony Blinken met with Chinese Vice President Han Zheng on Monday on the sidelines of the United Nations General Assembly, the latest in a series of meetings aimed at reducing tensions between the world's two largest economies.

The talks between Blinken and Han could help set the stage for a meeting between U.S. President Joe Biden and Chinese President Xi Jinping later this year.

They followed 12 hours of meetings last weekend between White House national security adviser Jake Sullivan and Chinese Foreign Minister Wang Yi in Malta, which both sides described as "candid, substantive and constructive."

"The world expects us to responsibly manage our relationship," Blinken said in brief remarks at the beginning of his meeting with Han. "The United States is committed to doing just that," he added.

"From the perspective of the United States, face-to-face diplomacy is the best way to deal with areas where we disagree, and also the best way to explore areas of cooperation between us," Blinken said.

Blinken, U.S. Commerce Secretary Gina Raimondo, Treasury Secretary Janet Yellen and Biden climate envoy John Kerry have traveled to China this year to thaw relations and ensure continued communication between the two countries amid tensions that flared after the U.S. military shot down a Chinese surveillance balloon that traveled over the United States.

Biden this month expressed disappointment that Xi had skipped a summit of Group of 20 leaders in India, but said he would "get to see him."

The next likely opportunity for Biden to hold talks with Xi is an Asia-Pacific Economic Cooperation summit in San Francisco in November, where U.S. aides for months have hoped to stage such a meeting.

Neither Blinken nor Han in their remarks explicitly mentioned whether such a meeting would materialize.

"Currently, China-U.S. relations face many difficulties and challenges," Han told Blinken, noting that China hoped the U.S. would make efforts to implement the consensus reached by the two countries' leaders and promote the stable development of relations.

"The world needs stable and healthy China-U.S. relations," Han said.

The U.S. and China are at odds over issues ranging from Taiwan to trade, fentanyl and human rights. Critics of the Biden administration have questioned its strategy of engaging China, warning that a failure to push back on provocations, including the recent China-linked hacking of senior U.S. officials' email, could embolden Beijing.

Federal Bureau of Investigation Director Chris Wray told a conference on Monday that China has a cyberespionage program so vast that it is bigger than all of its major competitors combined.

Ryan Hass, a China expert at the Brookings Institution, said the pace of high-level exchanges between Washington and Beijing suggested that efforts were "purposeful" and not just part of relationship management.

"I expect both sides are working to set the stage for a productive meeting between both leaders in November," Hass said.

(Reporting by Humeyra Pamuk and Michael Martina; Editing by Sandra Maler, Don Durfee and Sonali Paul)