The Dow Jones Industrial Averageended 0.61 percent higher on Wednesday at 26,405.76, its highest close since late January, while the S&P 500 gained 0.13 percent to 2,907.95.
The Nasdaq Composite dropped less than 0.1 percent, to 7,950.04, pulled down by a fall in Microsoft.
U.S. shares had been boosted by expectations that the impact of the Sino-U.S. trade war would be smaller than feared, with the U.S. fiscal policy package potentially outweighing any negative impact.
But analysts at Citi cautioned in a note that housing data out this week showed signs of weakness despite a headline jump.
Citi said housing starts had been strong, but building permits - a indicator of future activity - were at their lowest since May 2017.
"The housing market remains a specific point of weakness in the U.S. economy and while not in focus, it could be important... housing data on Tuesday wasn't encouraging on net."
The rally in global stocks has been accompanied by falls in U.S. bonds and the Japanese yen. The yield on benchmark 10-year Treasury notes, which on Wednesday touched its highest level since May 18, was at 3.0626 percent Thursday, compared with its U.S. close of 3.083 percent.
This week's rise in yields comes ahead of what is expected to be a hawkish meeting of the U.S. Federal Reserve next week.
The two-year yield, which is sensitive to market expectations of Fed rate hikes, was at 2.7949 percent compared with a U.S. close of 2.807 percent.
The dollar was flat against the yen at 112.26, and against the euro at $1.1673.
The dollar index, which tracks the greenback against a basket of six major rivals, was nearly unchanged at 94.558.
U.S. crude ticked up 0.4 percent at $71.43 a barrel, adding to a rise Wednesday after new data showed U.S. crude inventories fell 2.1 million barrels last week, its fifth weekly drawdown, to 394.1 million barrels.
That was the lowest level since February 2015.
Brent crude fell 0.1 percent to $79.31 per barrel.
A weakening dollar pushed up the price of gold on Wednesday, but the precious metal was flat on Thursday morning in Asia. Spot gold was trading at $1,203.61 per ounce.
(Reporting by Andrew Galbraith; Additional reporting by Herbert Lash in New York. Editing by Eric Meijer) ((Andrew.Galbraith@tr.com; +86 21 6104 1779; Reuters Messaging: email@example.com ; Twitter: https://twitter.com/apgalbraith))
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