"China's actions raise regional tensions and increases the risk of miscalculation, confrontation and accidents, and restraint is critically important on these issues, especially at this time," Hagel said in a joint news conference with the counterpart from Singapore Ng Eng Hen.
"The United States does not recognise the newly announced Air Defence Identification Zone (ADIZ), which I have noted before, and we urge China not to implement the ADIZ decision and we refrain from taking similar actions elsewhere in the region," he said.
"The United States remains committed to the rebalance to the Asia-Pacific in every way and to our important partnership with Singapore," he told reporters at the Pentagon.
China's ADIZ was one of the major topics of discussion between the two leaders.
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"I shared with the minister our deep concern about the Chinese announcement...And I think all the nations of Southeast Asia also are concerned," Hagel said.
"And these issues of ADIZ and the dispute in the South China Sea, East China Sea are realities that we're going to have to work through," he said, adding "Our commitment to our allies in this area remains strong. And we will honor those commitments. We will honor them in every way."
"But these issues have to be resolved carefully, diplomatically and peacefully," he added.
The Defense Minister of Singapore said the China-US relationship is the relationship that will impact all countries, as well as the stability.
"There will be strategic competition, but Secretary Hagel and I discussed at length how we need to use the platforms to make sure that reduce the risk of miscalculation, we don't precipitate tensions.
"And we talked about how we can take this forward using various platforms, whether it's the ASEAN Defense Ministers Meeting-Plus or the Shangri-La Dialogue, so that we avoid conflicts and precipitating tensions," the top official from Singapore said.