Beijing and Tokyo have had diplomatic relations for more than 50 years but friction has been building as China asserts its military presence around disputed territories in the region, and Japan boosts security ties with the United States and its allies.
In August, a Chinese military aircraft staged the first confirmed incursion by China into Japanese airspace, followed weeks later by a Japanese warship sailing through the Taiwan Strait for the first time.
And the neighbours' fraught 20th-century history was brought to the fore in a diplomatic row last month over the fatal stabbing of a Japanese schoolboy in southern China.
Xi nevertheless welcomed his new counterpart, Xinhua news agency reported, saying he hoped the "neighbours separated by a strip of water" could find common ground to "build a constructive and stable" relationship.
"It is in the fundamental interests of the two peoples to follow the path of peaceful coexistence, friendship for all generations, mutually beneficial cooperation and common development," Xi told Ishiba on Tuesday, according to Xinhua.
- 'Frank exchanges' -
Japan's new Foreign Minister Takeshi Iwaya said on Wednesday that Tokyo also wanted a "constructive and stable relationship" with China based on common interests.
But "what we need to assert will be asserted", and "as a major country, we seek China to behave responsibly", said newly nominated Iwaya.
"We are seeing attempts to unilaterally change the status quo in the East Asia region, so we need to build a system that can firmly deter such attempts," he added.
The minister said he hoped to meet his Chinese counterpart Wang Yi "as soon as possible" for "frank exchanges and dialogue", but a date had not yet been decided.
Japan's new Defense Minister Gen Nakatani called China "a serious concern" with its opaque military spending and robust naval activities.
"Our country is surrounded by various countries. In the worst-case scenario, it's possible that we face multiple crises at once," Nakatani told a press conference.
"We must be prepared for all kinds of circumstances," he said.
Beijing last week reacted angrily and lodged a complaint with Tokyo after a Japanese warship sailed through the Taiwan Strait.
While China claims jurisdiction over the body of water and over democratic Taiwan, the United States and its allies are increasingly crossing the 180-kilometre (112-mile) strait to reinforce its status as an international waterway.
Beijing's foreign ministry spokesman Lin Jian said China was "highly vigilant about the political intentions of Japan's actions".
China's Liaoning aircraft carrier also recently steamed between two Japanese islands near Taiwan for the first time.
Ishiba, 67, visited Taiwan in August and backs the creation of a regional military alliance along the lines of NATO, with its tenet of collective defence.
He outlined his policies at a news conference late Tuesday, warning that "the security environment surrounding our country is the most severe since the end of World War II".
Last month, the neighbours' old history resurged after the fatal stabbing of a 10-year-old schoolboy in the Chinese city of Shenzhen led to high-level diplomatic exchanges, with former prime minister Fumio Kishida demanding an explanation.
It remains unclear if the attack was politically motivated, although it happened on September 18 -- the anniversary of the 1931 "Mukden incident" or "Manchurian incident", which is known in China as a day of national humiliation and the beginning of a Japanese occupation.
Beijing and Tokyo were also at loggerheads last year after Japan began discharging treated water from the disabled Fukushima nuclear plant into the Pacific Ocean -- an operation the UN atomic agency said was safe.
But the release generated a fierce backlash from China, which branded it "selfish" and banned all Japanese seafood imports.
However, China last month said it would "gradually resume" importing the seafood.
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