Concerns about trade are weighing on the stock market — and it could get worse, veteran trader Art Cashin told CNBC on Tuesday.

The Dow Jones Industrial Average fell for the second straight day Tuesday and Cashin pinned the blame on tariff threats between the United States and the European Union. That, in turn, has traders thinking that "maybe the nearness of a deal with China is not there," said the UBS director of floor operations at the New York Stock Exchange.

And if there is no U.S-China deal, that doesn't bode well for stocks, Cashin noted. Traders have "built up hope" for an agreement, which has "put a nice prop under the market." It's done the same with oil, which has been rising along with stocks, he said on "The Exchange."

"If it began to look like a semipermanent trade war, the market would definitely sell off."

Just how much depends on how long the skirmish goes on. If there is just a "little disappointment we are not moving along in the manner we thought," then stocks could pull back 2% or 3%, Cashin predicted.

"If it looks like we are looking at two years or something like that, with us going nose to nose with some major trading partners, then I think the sell-off could be more severe."

Negotiations between the U.S. and China are ongoing. Last week, President Donald Trump said that "we'll know over the next four weeks" if there will be a deal. Meanwhile, Chinese Vice Premier Liu He, who met with Trump last week, said a new consensus has been reached between the two nations on the text of a trade agreement, according to China's official state news agency Xinhua.

However, the focus this week shifted to the European Union. On Monday, the U.S. threatened to impose retaliatory tariffs on EU goods in response to subsidies the 28-nation bloc granted Airbus. The World Trade Organization ruled last year that those subsidies caused "adverse effects" to the U.S. The EU responded to the U.S. threat by saying it was ready to retaliate in kind.

Also, the new trade agreement between the U.S., Canada and Mexico is not a done deal yet. It has yet to be passed by Congress.

For those looking for a safe place to hide out until the trade wars settle down, Cashin said some consumer names might be helpful. He also said some tech stocks could be a good bet, because they are not direct objects in the trade war.

— CNBC Holly Ellyatt contributed to this report.

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