The Asian giants have been at loggerheads over territorial disputes and historical animosity, but Xi said they should "put aside disruptions", the official news agency Xinhua said.
Their ties were "troubled by complications at times", it cited the Chinese president as saying, but they should seek to return to normal development for the sake of regional peace and stability.
For his part Abe described China as "an important friend of Japan's since long ago".
The tone of the two leaders' comments after a G20 summit in Hangzhou was a marked improvement on the last time they met on Chinese soil, on the sidelines of an APEC gathering in 2014, when they could barely conceal their mutual distaste.
Ties later thawed, but tensions have been rising again in recent months.
The relationship between the two powers is crucial to Asian stability, and Abe said they were "both responsible for the region's peace and prosperity as well as the global economy".
Just weeks before the summit, hundreds of Chinese fishing boats, accompanied by government ships, flooded into nearby waters, infuriating Tokyo and raising questions about Beijing's intentions for the relationship.
Meanwhile, Japan has weighed in on another Chinese territorial dispute in the South China Sea, where Beijing has built artificial islands capable of supporting military facilities.
Abe has vocally criticised China for rejecting a July ruling by an international tribunal that said its extensive claims to the strategically vital waters had no legal basis.
And Abe reiterated his stance, saying: "Any dispute has to be solved peacefully and diplomatically under international law, not through power or intimidation."
"Since we are neighbours, we have a variety of problems," he said. "So therefore, it is important to have dialogue."
The two agreed to accelerate talks on an air and sea communications hotline between their defence ministries, he added.
Last week Japan's defence ministry requested a record budget, including funds for an anti-ship missile system to defend the East China Sea islands.
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