Stocks rose on Tuesday following a strong session in which traders shrugged off a breakdown in peace talks between the U.S. and Iran, yet were optimistic that a deal between the two countries was still possible.

The S&P 500

gained 1.18% and closed at 6,967.38. The broad market index now stands less than 1% below its 52-week high. The Dow Jones Industrial Average

added 317.74 points, or 0.66%, to close at 48,535.99. The Nasdaq Composite

advanced 1.96% and ended at 23,639.08.