NEW YORK, June 2 (Reuters) - The Standard & Poor's 500 and Dow Jones indexes closed slightly higher on Tuesday as risk appetite, fueled by investor enthusiasm for artificial intelligence stocks, overshadowed tensions over the fate of U.S.-Iranian talks to reopen the Strait of Hormuz and end the months-long trade war.

The rise in the two indices was driven by gains in most of the 11 major sectors of the S&P 500, while the Russell 2000 index of small-cap companies outperformed its larger counterparts. The Nasdaq ended the session virtually unchanged.

Small-cap stocks were among the biggest beneficiaries, as investors continued to flock to artificial intelligence shares, providing some upward support. The Philadelphia Semiconductor Index rose during the session.

The software and services index closed lower after coming under pressure in recent months due to concerns about disruptions that could be caused by artificial intelligence.

Strong earnings results from Hewlett Packard Enterprise and a funding commitment from Alphabet have boosted investor confidence in the artificial intelligence development sector.

"The market looks quiet at first glance, but there are a lot of things going on behind the scenes, and that describes a large part of this year," said Mike Dixon, head of portfolio management at Horizon Investments in Charlotte, North Carolina.

He added, "There is a huge disparity in the entire AI infrastructure ecosystem... Markets may be on the cusp of one particularly strong and frenzied rally, as momentum continues to prevail."

Iranian media reported that Tehran is considering a proposed agreement to end the war with the United States, but has not been in contact with Washington in the past few days.

Media reports indicated that Iran is adopting a "tough" approach given what it considers a long record of US non-compliance with agreements, as well as a persistent lack of trust.

Meanwhile, Israel continues its strikes on Lebanon despite warnings from Tehran that the attacks threaten to derail the fragile truce.

Preliminary data showed the S&P 500 index rising 10.07 points, or 0.13 percent, to close at 7610.03 points, while the Nasdaq Composite index rose 8.78 points, or 0.03 percent, to 27095.59. The Dow Jones Industrial Average climbed 237.13 points, or 0.46 percent, to 51316.01 points.