Stocks rose on Tuesday after tumbling on the first day of the new quarter, but the market could still hit new lows in coming days, strategist Kenny Polcari told CNBC on Tuesday.
That "doesn't mean that all the concerns from yesterday are gone by any stretch of the imagination," the O'Neil Securities director told "Squawk on the Street." "It doesn't mean now that we've broken this level that we're not going to test lower again in the days ahead."
On Monday, the Dow sank more than 450 points, with the 30-stock index hitting a new low for the year. The S&P 500 and Nasdaq closed in correction territory amid the possibility of a trade war and fears surrounding the tech industry.
The major indexes recovered much of their losses on Tuesday as technology shares bounced back somewhat from the previous session. The Dow closed up over 1.6 percent, while the S&P 500 gained over 1.2 percent and the Nasdaq closed up 1.3 percent.
"You may get a bit of a dead cat bounce today, which is what it feels like right now," Polcari said. "But I wouldn't be so sure the volatility is over just yet."
The market may "test some lows" as it searches for a new leader other than the FANG stocks, said Jefferies chief market strategist David Zervos. FANG stocks include Facebook, Amazon, Netflix and Google.
"The thing that led us for a long time is not leading us anymore," Zervos told "Squawk on the Street" on Tuesday. "We're either going to search for a new leader or going to search for breadth."
Tech has been the best-performing sector in the S&P 500 over the past 12 months, rising nearly 23 percent through Tuesday's close. But the sector has been under pressure recently because of growing concerns it could be hit with regulation.
"Maybe we can let the leaders of the past find some stability or even a little bit of weakness and pass the baton to a market with more breadth that's got tailwinds from two wonderful sources — deregulation and lower taxes," Zervos added.
"The market's got to make that transition. And it's a hard one because (tech has) been in this leadership story for many, many years."
Investors' concerns surrounding global trade also continued to rumble on. China recently announced that it would be implementing new tariffs on 128 U.S. products, including fruit and meat, in response to the U.S. levies on steel and aluminum.
— CNBC's Fred Imbert and Alexandra Gibbs contributed to this report.