Malaysia's state-run oil firm Petronas operates oil and gas fields in the sea within its exclusive economic zone.
But China claims almost all of the economically vital waterway despite competing claims from other countries and an international court ruling that its assertion has no legal basis.
"What we did in terms of oil exploration is certainly within our waters," Anwar told reporters travelling with him on a visit to Russia.
However, he struck a conciliatory tone, describing China as a friend and saying both countries would discuss the issue amicably.
"We will probably respond to China in explaining our position that we have never intended to be in any way provocative, unnecessarily hostile," Anwar said.
"China is a great friend. But we will of course have to operate in our waters and secure economic advantage, including drilling for oil, in our territory."
A Philippine news website last week published what it said was a leaked diplomatic note in which China demanded that Malaysia stop all oil and gas activities off Sarawak state on Borneo island.
Beijing said in the note that Malaysia was encroaching on Chinese territory.
Malaysia's foreign ministry has called for an investigation into the leak but has not denied the document's authenticity.
The Chinese foreign ministry told AFP it was "astonished" by the Philippine media report, saying there was an "ulterior motive" to it.
"As countries directly concerned in the South China Sea issue, China and Malaysia have maintained close communication on properly handling their differences and disputes," it said.
Anwar said it was a matter of Malaysia's "economic survival" that the exploration continued.
Malaysia was open to discussing the matter with China "but it does not mean that we have to stop".
"If they continue with the dispute, then we will have to listen and they will have to listen. But it should not mar the excellent bilateral relations between these two countries," Anwar added.
The Philippines and China have had repeated confrontations recently in the South China Sea, considered a regional flashpoint because it could drag Manila's mutual defence treaty ally the United States into a conflict.
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