U.S. stocks closed lower on Tuesday, snapping a four-session winning streak, as Wall Street shifted its focus from Brexit to the uncertainty over the timing of a next rate hike.

The Dow Jones Industrial Average was down 108.75 points, or 0.61 percent, to 17,840.62. The S&P 500 lost 14.40 points, or 0.68 percent, to 2,088.55. The Nasdaq Composite Index shed 39.67 points, or 0.82 percent, to 4,822.90.

Investors will keep a close eye on Friday's nonfarm jobs report this week for more clues on the U.S. Federal Reserve's next rate hike.

"This week's highlight is the June employment report," said Chris Low, chief economist at FTN Financial, Tuesday.

New York Fed President William Dudley, a voting member of the Federal Open Market Committee (FOMC), said Tuesday that the Fed could be patient on raising interest rates due to low inflation and uncertainties over prospects for the U.S. economy, including Britain's vote to leave the European Union, according to the CNBC.

The CBOE Volatility Index, often referred to as Wall Street's fear gauge, increased 5.48 percent to end at 15.58 on Tuesday.

U.S. stocks market was closed Monday for the Independence Day holiday.

U.S. stocks rallied in the past week as global markets rebounded from the previous week's losses after Britain's vote to leave the European Union.

Markets showed a sign of recovery earlier last week across the globe after a record 3 trillion U.S. dollars in market capitalization was wiped off in the post-Brexit plunge.

U.S. stocks all closed nearly 1.5 percent higher from Tuesday to Thursday last week. Meanwhile, European stocks had also recovered, with Britain's benchmark FTSE 100 Index being completely recovered to pre-vote levels.