In 3.31pm trading in New York, the Dow Jones Industrial Average gained 0.4 per cent, while the Nasdaq Composite Index climbed 0.5 per cent. In 3.16pm trading, the Standard & Poor's 500 Index rose 0.4 per cent.
The Dow moved higher as gains in shares of Home Depot and those of Chevron, recently up 2.5 per cent and 2.4 per cent respectively, outweighed declines in shares of United Technologies and those of Verizon, down 1.6 per cent and 1 per cent respectively.
"You have opposing forces kind of keeping the market from breaking out to a new high, but yet the fundamental data seem to be keeping it from breaking down and selling off significantly," Walter Todd, chief investment officer of Greenwood Capital in Greenwood, South Carolina, told Reuters.
"You kind of have these opposing forces pushing on each other and keeping the market in a very narrow range," Todd said.
The latest US economic data were upbeat. An Institute for Supply Management report showed its non-manufacturing activity index rose to 55.3 in August, up from 53.9 in July, which was the lowest level in 11 months.
Separately, a Commerce Department report showed the trade deficit widened 0.3 per cent to US$43.7 billion in July.
"The US economy carried a little more momentum than originally thought," Jennifer Lee, a senior economist at BMO Capital Markets in Toronto, told Reuters. "However, some of that momentum will be blunted by, for starters, Hurricane Harvey."
In Europe the Stoxx 600 Index ended the session with a 0.1 per cent gain from the previous close. France's CAC 40 Index rose 0.3 per cent and Germany's DAX Index climbed 0.8 per cent. The UK's FTSE 100 Index fell 0.3 per cent.
European Central Bank policy makers gather on Thursday. Investors will closely eye ECB President Mario Draghi's post-meeting comments including on the euro.
"Despite the single currency's rise to a three-year high in trade-weighted terms, the president has not yet made any significant attempts to talk it down," Capital Economics economist Jennifer McKeown said in a note.
"If he wanted to pull the euro down, he could state that the recent increase has reflected geopolitical factors and that the exchange rate now does not properly represent the fundamental outlook for the euro-zone economy or monetary policy," McKeown noted. "He could even downplay expectations of QE tapering next year."
"We ... think that the immediate risks to the euro are skewed to the upside," McKeown said, adding that her forecast that the currency will end this year and next at US$1.15 "is reliant on renewed tightening by the US Fed and some easing of geopolitical concerns and related safe haven flows.