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Five minutes into trade, the Dow Jones Industrial Average rose 36.11 points (0.25 percent) to 14,332.35, after setting a fresh all-time closing high Wednesday at 14,296.24.
The broad-based S&P 500 gained 3.42 (0.22 percent) at 1,544.88, while the tech-rich Nasdaq Composite rose 4.40 (0.14 percent) to 3,226.77.
Traders remained cautious but there were no signs yet that investors believed the market was overvalued.
"The lack of selling interest reflects concerns about missing out on further gains and getting mentally whipsawed again by the sight of the market quickly bouncing back from any type of dip," said Patrick O'Hare of Briefing.com.