The Nikkei 225 index <.N225> rose 0.89% to 23,346.05, back above the 25-day moving average of 23,275, a key technical level.
The broader Topix gained 0.5% to 1,711.80, just shy of the 13-1/2-month high of 1,719.57 hit late last month.
Topix Core 30, made up of top 30 firms on the main board, hit a 14-month high.
Trump said negotiations with China were going "very well," fanning the positive mood sparked after a Bloomberg report that Washington and Beijing were closer to agreeing how many tariffs would be rolled back.
Steelmakers were the biggest beneficiary of latest splurge in optimism, with the Tokyo Stock Exchange's steel and iron index <.ISTEL.T> gaining 2.9%. It was the top performer among 33 industry sub-indexes.
Nippon Steel rose 3.8%, JFE Holdings gained 3.4% and Kobe Steel climbed 2.5%.
Semiconductor related shares also outperformed the benchmark, including Sony, which rose the most in over a year. It later pared some gains to rise 0.1%.
TDK rose 2.1% and Lasertec gained 0.6% to hit an all-time high.
Murata Manufacturing rose 1.1%, helped by report by Nikkei business daily that the company has developed new electronic parts to be used for 5G smartphones.
Nintendo edged up 0.1% and stayed near its 1-1/2-year high, supported by hopes of earnings boost from Switch game console it will launch next week in China.
Among drugmakers, Astellas Pharma gained 2.4%, while Daiichi Sankyo rose 1.8%.
(Reporting by Tokyo Markets Team; editing by Uttaresh.V)