Thursday's stock market rally appeared to be the most credible rebound Wall Street has seen during the past few weeks of downward swings and weak gains, UBS' Art Cashin told CNBC on Thursday.
"We tried for two days with a very heavily oversold market to produce a rebound," Cashin said on "Squawk on the Street." "You had a lackluster blip up on Tuesday. Wednesday, you've got no follow through."
Cashin said three factors played into Thursday's better showing: Traders bought discounted stocks, others covered short positions, and the yield on the 10-year Treasury note surpassed 2.67 percent,
If the market can break through a band of resistance at 1,771 points for the S&P, he added, the rally could continue,
(Read more: US stock indexes rally as growth concerns ebb)
"You could give this legs and it could last for few days," Cashin said. "We're in a very critical area right here."
—By CNBC's Jeff Morganteen. Follow him on Twitter at @jmorganteen and get the latest stories from "Squawk on the Street."