The request emerged during talks between visiting Japanese Foreign Minister Fumio Kishida and Vietnam's Prime Minister Nguyen Xuan Phuc and Foreign Minister Pham Binh Minh, a Japanese spokesman said.
"Vietnam wants new vessels," Masato Otaka told reporters, adding that timing, methods of delivery, costs and quantity of vessels had not yet been decided.
Vietnam has been modernising its military, and recently bought six advanced Kilo-class submarines from Russia.
Russia and India are the main source of advanced weapons, training and intelligence cooperation. Hanoi is also building ties with the United States and its Japanese, Australian and Filipino allies, as well as Europe and Israel.
"Vietnam feels it needs to strengthen its coastguard generally, and that's why we've responded," Otaka told reporters, adding that the vessel delivery "was not directly linked to the South China Sea (the East Sea of Vietnam)".
On Friday Kishida is scheduled to attend a joint government meeting that will mainly focus on economic cooperation, Otaka said.
Japan is the second-biggest investor in Vietnam after South Korea, with existing projects totalling $39 billion as of April 2016, based on Vietnam's government data.
Two Japanese warships visited Cam Ranh Bay in central Vietnam in April, the first port call of its kind.
Japan also has warming relations with the Philippines, with which it signed a deal last year on defence equipment and technology.
China claims almost the entire the East Sea, believed to have huge deposits of oil and gas, and is building islands on reefs to bolster its claims. Brunei, Malaysia, the Philippines, Taiwan and Vietnam also have claims to parts of the waters, through which about $5 trillion in trade is shipped every year.
Tokyo has no claims in the waterway, but worries about China's growing military reach into sea lanes through which much of Japan's ship-borne trade passes.