The benchmark Nikkei 225 index was up 1.02 percent or 207.05 points at 20,468.09 in early trade, while the broader Topix index was up 0.92 percent or 13.64 points at 1,491.67.
Trump breathed some optimism into global markets when he told reporters at a summit in France that Washington and Beijing would soon return to the bargaining table, appearing to change tack yet again.
"China called last night... said let's get back to the table. So we'll be getting back to the table," he said on Monday, adding that "they want to make a deal".
The dollar fetched 106.92 yen in early Asian trade, up from 106.08 yen in New York and 105.24 yen in Tokyo on Monday.
In Tokyo, automakers were among the winners, with Toyota trading up 0.48 percent at 6,902 yen, Honda gaining 1.26 percent to 2,484 yen and Nissan rising 0.52 percent to 652.2 yen.
Other blue-chip exporters were broadly higher. Sony rose 0.46 percent to 5,870 yen and Panasonic added 0.68 percent to 812.3 yen.