The stock market appears to be searching for its lowest point after a two-day plunge, closely followed trader Art Cashin told CNBC on Tuesday.

Cashin, 76, UBS director of floor operations at the New York Stock Exchange, cited his decades of experience on Wall Street to support his case.

"Markets remain thin, and they remain volatile," Cashin told "Squawk on the Street." "And quite frankly, after doing this for 50 years, that's just what you need for a bottoming process to succeed."

Investors should not jump ahead of themselves, Cashin contended. "Let the market tell you where it's going by zigzagging back and forth and holding the previous levels."

Stocks traded in a wide range Tuesday as the major indexes tried to recover from a sell-off. The Dow Jones industrial average traded higher shortly after the open before turning negative again, trading down as much as 900 points early Tuesday.

Monday was the worst day for the Dow and since August 2011 as well as the biggest single-day point drop for the Dow in history. The Dow broke below 25,000 and erased its 2018 gains.

Cashin said last week that the wage number in January's stronger-than-expected jobs report was unhelpful to an already worried stock market.

Before the jobs report, investors were concerned about rising interest rates and political risk, Cashin said, including the release of a Republican memo alleging FBI bias against President Donald Trump.

On Monday afternoon, Cashin said the market "snapped like a twig" and the roller-coaster ride is probably not over.

Cashin began his career at Thomson McKinnon in 1959. In 1964, at age 23, he became a member of the NYSE and a partner in P.R. Herzig & Co.