The S&P rose more than half a percent to close at 3,039, almost 4 points higher than the most recent record set in July.
The Dow Jones Industrial Average was also up, closing less than 1 percent off its own all-time high, while the tech-heavy Nasdaq index rose a little over 1 percent.
South Korea's benchmark KOSPI also started strong, but investors took a wait-and-see approach in terms of a Fed rate cut, leaving the index flat at about 20-92.
The U.S. gains come after President Trump told reporters on Monday that a significant part of the trade deal with China could be signed ahead of schedule.
This the "Phase One" agreement he said was reached, essentially, earlier this month in Washington.
Trump said it will help farmers, and in his words "take care of a lot of the banking needs."
The U.S. and China are widely believed to be looking to sign the deal next month in Chile on the sidelines of the APEC summit.
And possibly to help make that happen, the U.S. Trade Representative announced Monday that it's considering another delay in the tariffs due to take effect this December.
Those would affect Chinese goods worth around 34 billion dollars.
The agency will take comments on that proposition in November before making a final decision.
Hong Yoo, Arirang News.