The U.S. stock market is rising as it catches up with others around the world that climbed the day before, when President Donald Trump said negotiations were "proceeding nicely" with Iran on ending their war. The S&P 500 rose 0.6% early Tuesday after trading resumed following Monday's holiday. The Dow Jones Industrial Average edged up 44 points, and the Nasdaq composite climbed 0.9%. All three indexes are at or near their all-time highs. The price for a barrel of Brent crude, the international standard, rose 3%. Treasury yields moved lower in the bond market. European and Asian markets were mixed.