By Hyonhee Shin and Josh Smith
SEOUL (Reuters) -Senior diplomats from&nbsp;South&nbsp;Korea,&nbsp;China&nbsp;and&nbsp;Japan&nbsp;agreed on Tuesday that their countries' leaders would meet at the "earliest&nbsp;convenient&nbsp;time", Seoul's foreign ministry said after a rare meeting aimed at kickstarting trilateral exchanges.
The three countries had&nbsp;agreed to&nbsp;hold&nbsp;a&nbsp;summit&nbsp;every year starting in 2008 to foster regional cooperation, but that initiative has been frayed by bilateral feuds and the COVID-19 pandemic. The last&nbsp;summit&nbsp;was in 2019.
Seoul's foreign ministry said in a statement that specific dates remained under discussion and that the countries' foreign ministers would meet "in a couple of months".
South&nbsp;Korea&nbsp;is this year's host for three-way meetings and has proposed a&nbsp;summit&nbsp;in late December,&nbsp;Japanese broadcaster TBS reported.
Japan's foreign minister, Yoko Kamikawa, said the three countries share the need to restart high-level talks, including&nbsp;summits, "as soon as possible".
"I believe it is very valuable to discuss the various challenges the region faces," she told a briefing in Tokyo.
The latest meeting was seen partly intended to assuage Beijing's concerns over the two U.S. allies' tightening cooperation after Seoul and Tokyo&nbsp;agreed this year to end legal, diplomatic and trade disputes over issues dating to&nbsp;Japan's 1910-45 occupation of&nbsp;Korea.
"We unanimously believe that carrying out cooperation is in the common interests of the three parties," Chinese foreign ministry spokesperson Wang Wenbin said on Tuesday. "We should work together to strengthen practical cooperation ... and make new contributions to regional peace, stability, and prosperity."
South&nbsp;Korean President Yoon Suk Yeol and&nbsp;Japanese Prime Minister Fumio Kishida have taken steps to mend ties and in August held a historic trilateral&nbsp;summit&nbsp;with U.S. President Joe Biden, where the three vowed to boost cooperation, including on defence and economic security.
A senior&nbsp;South&nbsp;Korean official said&nbsp;China&nbsp;has been proactive in seeking trilateral cooperation and arranging meetings since bilateral ties soured over the deployment in 2017 of a U.S. THAAD anti-missile system in&nbsp;South&nbsp;Korea.
"I'm sure there should be some discomfort on their side regarding our increasingly close trilateral security partnerships with the United States and&nbsp;Japan," the official said, speaking on condition of anonymity because of the sensitivity of the situation. "There seems to be a view there that they need to properly manage bilateral ties with us, as they saw how their THAAD responses backfired and fuelled anti-China&nbsp;sentiment to serious levels."
Beijing will most likely look to leverage trilateral trade ties to counterbalance the U.S. friend-shoring strategy, promote people-to-people exchanges, and enhance communication and dialogue with Seoul and Tokyo on security and defence matters, said Tong Zhao, senior fellow at the U.S.-based Carnegie Endowment for International Peace.
Japan&nbsp;and&nbsp;South&nbsp;Korea&nbsp;have an interest in avoiding conflicts and maintaining a stable security relationship with&nbsp;China, and Beijing's assistance in slowing down, if not halting, North&nbsp;Korea's extensive nuclear development program, he added.
"These shared interests open up new avenues for strategic communication, confidence-building, and measures to prevent crises," Zhao said.
China's premier has traditionally attended the trilateral&nbsp;summits, and&nbsp;South&nbsp;Korea&nbsp;is also pushing for a separate visit by President Xi Jinping.
The latest meeting involved&nbsp;South&nbsp;Korean Deputy Foreign Minister Chung Byung-won,&nbsp;Japanese Senior Deputy Foreign Minister Takehiro Funakoshi, and Nong Rong,&nbsp;China's assistant minister of foreign affairs.
(Reporting by Josh Smith and Hyonhee Shin in Seoul; Additional reporting by Liz Lee in Beijing, Soo-hyang Choi in Seoul and Sakura Murakami and Satoshi Sugiyama in Tokyo; Editing by Gerry Doyle)

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South Korea, Japan, China agree to hold summit at 'earliest convenient time'