Bishop, who is on a visit to the Philippines, said she discussed the matter with her Filipino counterpart Albert del Rosario.
There have been heightened tensions between China and its neighbours -- including the Philippines -- because of disputes over maritime territory.
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"In the case of the South China Sea, we support ASEAN objectives in concluding a Code of Conduct with China and we hope that there will be some early progress on that," she said.
"We urge all sides not to escalate tensions," she added.
ASEAN has been trying for more than a decade to secure agreement from China on a legally binding code of conduct aimed at reducing tensions and the risk of violence in the South China Sea.
Among ASEAN members are Brunei, Malaysia, Taiwan, the Philippines and Vietnam, which along with China, have claims to parts or all of the South China Sea.
China claims almost all of the South China Sea, even up to the borders of its neighbours.
Bishop stressed that her country was not taking any side in the dispute, and urged that all issues should be resolved "peacefully".
Bishop said the South China Sea was a key interest to Australia since 60 percent of its exports and 40 percent of its imports passed through the area.
The Philippines has been seeking more international support to challenge China's claims to the South China Sea.
Del Rosario meanwhile said the Philippines had been forced to seek UN arbitration because it had "exhausted all (other) possibilities," in arguing its case with China.
He also said that the Philippines and Australia would be boosting their defence cooperation especially after a "status of visiting forces agreement" between the two countries went into effect in 2012.
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