China rejected Blinken's comments, which he made in an address in a video conference with foreign ministers from the Association of Southeast Nations (ASEAN), as irresponsible and aimed at provoking discord.
Blinken also said the United States had "deep concerns" about the situation in Myanmar and urged the group to take action to end violence and restore democracy there.
The meeting with the 10-member bloc, which includes Myanmar, is the first since the Biden administration took office in January and comes amid concerns among diplomats and others that Washington has not been paying sufficient attention to a region that is crucial to its strategy to counter an increasingly assertive China.
Myanmar's junta has shown little sign of heeding what ASEAN called a five-point consensus, reached in April, which seeks an end to violence, political talks and the nomination of a regional special envoy to Myanmar.
Blinken urged ASEAN to take "immediate action" on the consensus and appoint the envoy, State Department spokesperson Ned Price said in a statement.
Blinken asked for the release of all those "unjustly detained" in Myanmar and the restoration of its democratic transition, Price said.
China said the comments were aimed at derailing regional peace and stability.
"It is extremely irresponsible of the U.S. to deliberately provoke controversy over territorial sovereignty and maritime rights in the South China Sea, sow discord among China and ASEAN countries," Chinese foreign ministry spokesman Zhao Lijian told a briefing in Beijing.
Trillions of dollars in trade flow every year through the waterway, which also contains rich fishing grounds and gas fields.
In addition to the South China Sea, the Mekong River has become a new front in U.S.-China rivalry, with Beijing overtaking Washington in both spending and influence over downstream countries at the mercy of its control of the river's waters.
Price said Blinken "pledged continued U.S. support for a free and open Mekong region under the Mekong-U.S. Partnership".
"We understand that multilateralism was not a key focus for the previous administration, but the Biden administration's embrace of multilateral cooperation is a welcome development," Hishammuddin said, according to a copy of his delivered remarks.
"This path is the only way forward to ensure stability, peace, prosperity and security for our region."