Addressing a joint press conference after talks held in Hanoi, Prime Minister Phuc said: "We are deeply concerned about the recent complicated developments in the East Sea and agree to cooperate in maintaining peace, stability, security, safety and freedom of navigation and overflight."
The East Sea is referred to internationally as the South China Sea.
Morrison called for principles of international law to be upheld in the region.
"Principles like freedom of navigation, freedom of overflight, to ensure nations can pursue the development opportunities which exist within their EEZ and sea boundaries, and can go about that business in a way which is uninhibited," Morrison explained.
The Australian premier is on a three-day visit to Vietnam that will wrap up Saturday.
The statements by the two prime ministers were made in the context of Chinese oil survey vessel Haiyang Dizhi 8 and escort vessels illegally re-entering Vietnamese waters near the Vanguard Bank in the southern area of the South China Sea on August 13.
The survey vessel and its escorts had left Vietnam’s exclusive economic zone (EEZ) and continental shelf on August 7 after occupying Vietnamese sea territory for about a month.
The U.S. State Department had said Thursday it was deeply concerned about China’s interference in oil and gas activities in waters claimed by Vietnam, and that the deployment of the vessels was "an escalation by Beijing in its efforts to intimidate other claimants out of developing resources in the South China Sea."
During their talks, the prime ministers of Vietnam and Australia agreed to cooperate and work to maintain peace, stability, security, safety, freedom of navigation and aviation. They also reaffirmed their commitment to avoiding use of force and threats to use force.
Both sides also stressed that maritime disputes must be settled in accordance with international laws and called for a full implementation of the 2002 Declaration on the Conduct of Parties in the South China Sea, as well as an early conclusion to a legally binding Code of Conduct in the South China Sea.
Morrison is the first Australian PM to officially visit Vietnam after the two countries upgraded their relationship to a strategic partnership in March last year.
Vietnam and Australia established diplomatic relations in 1973.
Bilateral trade rose 19.4 percent in 2018 to $7.72 billion, according to Vietnam Customs.
Australia is the largest foreign coal supplier to Vietnam, which is increasingly reliant on the fossil fuel for power generation to meet its fast-growing economy. Coal shipments from Australia to Vietnam more than tripled in the January-July period from a year earlier to 8.51 million tons, according to customs data.
"Australia and Vietnam are friends and, today, to use Australian parlance, we've gone from friends to mates," Reuters reported Morrison as saying.
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