Minister Wang Yi made the remarks during a visit to Sydney on Sunday, referencing Prime Minister Tony Abbott's comment last year that Japan was Australia's "closest friend in Asia".
Speaking through a translator, Mr Wang acknowledged that China "may not be Australia's closest friend at the moment, but we can surely become your most sincere friend".
He added that Australia was a "key co-operation power" for China in the Asian region.
"China welcomes and supports Australia to further understand Asia and to integrate into Asia," he said.
"And of course, we would also like Australia to play an active role as a bridge and as a link between the East and the West."
Ms Bishop said the bilateral talks came at a time of "great global challenge" and were an opportunity to discuss the movement of citizens from the two countries to Iraq and Syria to fight for violent jihadist groups such as the Islamic State.
"The conflict in Syria and Iraq affects both our nations, for foreign fighters are leaving our shores to take part in the brutal and bloody conflict in the Middle East," she said.
"Our meeting together affords us an opportunity to discuss ways that we together can combat terrorism and extremism such as we've seen with the emergence of ISIL," she said.
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