The Japanese markets were closed on Monday for a holiday.
Details are still being finalized, but that includes a halt to US tariff hikes coming into effect this week. Trump also told reporters that intellectual property, financial services and agricultural procurement are included in the deal.
Trump also suggested that he meet Chinese President Xi Jinping at next month's APEC summit in Chile.
Meanwhile, investors were drawing on trade data from China that fell below analysts' expectations.
Imports from September fell by 8.5% – well below the 5.2% decline forecasted by analysts.
Exports are likely to continue in the months ahead. Friday's limited trade agreement and the lack of higher tariffs should only have a "marginal impact" on export growth, Martin Lynge Rasmussen, China's economist for Capital Economics, wrote in a research note Monday.
He added that while imports may be picking up a little in the short run, they are also unlikely to suffer a sharp setback since domestic demand is soft.