"I think that will give the market a sense that they cleared another hurdle and maybe we can get back to an honest rally," Cashin, UBS director of floor operations at the New York Stock Exchange, said on "Squawk on the Street."
Cashin said that any more weakness in the market could send the S&P 500 down to as low as 2,822. But a bounce from there could signal sustainable strength in stocks, he added. The index opened Wednesday at 2,861.
Shortly after Wednesday trading began on Wall Street, the S&P 500 dipped and then climbed past 2,880 in fits and starts as the 30-year Treasury yield went below 2% again, hitting a record low.
In August, as of Tuesday's close, the S&P 500 was down nearly 3.75%, risking a second monthly decline in 2019. However, the index so far this year was still up 14.5% and just over 5% off July's all-time highs.
Cashin also responded to President Donald Trump's Wednesday morning tweet, in which he said the Federal Reserve "cannot 'mentally' keep up with the competition — other countries."
Cashin said traders won't react much, especially compared with past Trump posts that have caused the stock market to drop.
"That kind of tweet is relatively harmless. He can abuse the Fed all he wants," Cashin said. "What spooks the markets is if he gets into trade talk again."
The president has repeatedly called for the central bank to lower interest rates further.
The market expects the Fed to cut rates again next month, after reducing the cost of borrowing money in July for the first time in more than a decade. Central bankers hiked rates four times last year.