By Agence France-Presse
The Nikkei 225 index rose 2.56 percent, or 556.01 points, to 22,243.66, finishing the week 5.0 percent higher, while the broader Topix index was up 1.64 percent, or 26.71 points, at 1,658.76, a gaining of 3.93 percent from last Friday.
"Hopes of a breakthrough on the US-China trade war dominated the market," said Shinichi Yamamoto, broker at Okasan Securities in Tokyo.
Tokyo and other Asian shares marked sizeable gains after Donald Trump hailed positive talks with Chinese President Xi Jinping and a report said he had asked officials to draw up a draft bill as he eyes a potential trade deal between the two.
"The positive sentiment encouraged investors to buy on dips following recent declines," Yamamoto told AFP.
A weak yen also helped sustained bottomline support for the market, brokers said.
The dollar fetched 112.96 yen in Asian afternoon trade, against 112.62 yen in New York late Thursday.
"The top focus for next week is US mid-term elections," Yamamoto said, adding that the market will also focus a US Federal Reserve meeting.
NTT Docomo jumped 4.49 percent to 2,535 yen after a 14.71 percent plunge Thursday that followed its announcement it would cut fees under government pressure.
Its rival KDDI was up 2.11 percent at 2,410 yen after it reported six-months to September results in line with market expectations. It also confirmed a tie-up with online retailer Rakuten.
But Japan Airlines fell 0.60 percent at 3,923 yen after news its pilot was arrested before a flight for being drunk and almost 10 times the legal alcohol limit for a pilot.
Its rival All Nippon Airways rose 0.77 percent to 3,764 yen. Shortly after the market closed, ANA said its first-half operating profit fell 8.6 percent on increased costs.
Suzuki Motor dropped 2.51 percent to 5,501 yen after it reported 136 billion yen net profit for the six months to September and disappointed investors with lower-than-expected second-quarter operating profit.