Multiple US media reported this week that Austin had hoped to meet his Chinese counterpart Dong Jun at a regional summit in Laos as part of efforts to maintain military contact between the two superpowers.
Austin reportedly said China had declined the meeting, calling the decision "a setback for the whole region".
Beijing hit back Thursday, saying "the responsibility for not holding a meeting... lies solely with the US side."
"The US can't damage China's core interests on the Taiwan question while at the same time conducting exchanges with the Chinese military as if nothing had happened," defence ministry spokesperson Wu Qian said in an online statement.
China and the US have butted heads in recent years over Taiwan, the self-ruled island that Beijing claims as part of its territory and has refused to rule out the use of force to seize one day.
On Saturday, President Xi Jinping warned his outgoing US counterpart Joe Biden that support for Taiwan was a "red line that must not be challenged" during a meeting on the sidelines of the Asia-Pacific Cooperation summit in Peru.
The US approved a $2 billion arms sale package for Taiwan in October.
Xi also said Beijing was ready to work with the incoming administration of Biden's successor, Donald Trump, whose first term in office yielded a damaging trade war between the world's two largest economies.
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