Cashin: I won’t believe in the stock rally until the S&P hits 1,950

The current stock market rally is encouraging because it's broad-based, but it has yet to prove itself, Art Cashin said Wednesday.

Stocks were rallying for a third day Wednesday. The Dow Jones industrial average jumped more than 200 points, and the S&P 500 rose above 1,920, a critical early support level, according to Cashin.

However, equities have a bit further to go before they make a believer out of the director of floor operations at the New York Stock Exchange for UBS.

"It will prove itself if it gets above 1,950. For now we've taken a healthy leap forward. As I say, it's broad, so you've got to appreciate that, but I won't declare 'in' until we talk about 1,950," he told CNBC's "Squawk on the Street."

The fact that cyclical stocks — including consumer discretionary, industrials and financials — managed to grind higher after getting beaten up suggests short covering is at least partly behind the rally, he said.

Shares also got a boost from surging crude futures, which extended gains after Iran's oil minister said the country supports a plan floated this week by fellow producers Saudi Arabia, Russia, Venezuela and Qatar to freeze output at January levels.

While U.S. crude rose above the critical $30-per-barrel mark, it is important that the commodity proves it can hold those gains, Cashin said. Few people believe talks between OPEC members and non-OPEC producers to stem oil price losses will ultimately be fruitful, he said.

Barry Bannister, chief equity strategist at Stifel Nicolaus, said Wednesday on "Squawk on the Street" that a freeze would not be particularly helpful because it caps production near maximum output. Further, he said he worries about supply from the "Shiite axis" of Iran and Iraq.

Both Iran and Iraq have ramped up production and are politically aligned against top oil exporter Saudi Arabia, the predominant Sunni Muslim power in the region.

The S&P 500 can likely rise above the mid-1,900 level, but gains will be capped because the Federal Reserve must eventually raise interest rates, Bannister said.

He chalked up the rally to the perception that the Fed will not hike interest rates at least until the second half of the year, and the sense that China has achieved some stability in its currency, easing fears that it will export deflation to the rest of the world.

The market is likely to progress up in the medium term as calm sets in, Samantha Azzarello, global market strategist at JPMorgan Funds, said Wednesday.

"I'm not going to say the market is irrational, but at the same time, the amount of sell-off we've seen, we just don't think it's justified," she told "Squawk on the Street."