U.S. stocks advanced further in early trading on Tuesday, with the S&P 500 index reaching a new intraday high. Traders are assessing the prospects of a potential agreement between the United States and Iran to end the conflict.

The Dow Jones Industrial Average rose 77.47 points, or 0.15%, to 50,657.17. The Nasdaq Composite gained 297.46 points, or 1.13%, to 26,641.43. The S&P 500 increased by 53.52 points, or 0.72%, to 7,526.99. During Tuesday's early session, the S&P 500 climbed to a peak of 7,529.04, setting a new intraday record. U.S. markets were closed on Monday for the Memorial Day holiday. The primary driver behind Tuesday's improved market sentiment was signals of easing tensions in the Middle East. The memory chip sector was a standout performer, with Micron Technology benefiting not only from the improved macro sentiment but also from recent public praise by former President Trump. Concurrently, demand for AI infrastructure remains robust. UBS raised its year-end target for the S&P 500 to 7,900 last week, citing the seemingly insatiable demand for data center infrastructure as a core driver. According to Iran's Tasnim news agency, Tehran is seeking to unfreeze approximately $24 billion in overseas funds as part of the negotiations. Former U.S. Secretary of State Marco Rubio indicated that an agreement could take several days to finalize, while former President Trump stated on social media that the talks were progressing well. Sources familiar with the matter suggest that the U.S. and Iran could reach a 60-day ceasefire agreement this week, with plans to restore free passage through the Strait of Hormuz to pre-war conditions on the 30th day after the deal is signed. However, analysts caution that while the outlook for U.S.-Iran talks appears optimistic, minor clashes occurred over the weekend, indicating the situation remains fragile and market sentiment could reverse at any time. Former U.S. President Trump stated on Monday that negotiations to end the war with Iran were "progressing well." However, he also warned that the U.S. could launch an offensive if the talks break down. Additionally, the U.S. military reported conducting a "self-defense" strike in southern Iran early Tuesday. U.S. Central Command spokesman Tim Hawkins stated that targets included missile launch sites and Iranian vessels attempting to lay mines. He added that the U.S. exercised "restraint" during the "ongoing ceasefire period" between the two countries. Brent crude oil prices rose on Tuesday as the U.S. military strike in southern Iran and mixed signals from former President Trump regarding the negotiations kept traders on edge. As of 7:59 a.m. ET, the international benchmark Brent crude was up 3% at $99.03 per barrel. U.S. West Texas Intermediate crude for July delivery was down 4% from Friday's close at $92.73 per barrel. The U.S. military stated that its self-defense strike in southern Iran targeted vessels suspected of attempting to lay mines and missile launch positions. U.S. Central Command said these actions were intended to protect its forces from threats posed by Iranian forces. Adam Crisafulli of Vital Knowledge wrote, "The market consensus still expects some form of formal de-escalation agreement between Washington and Tehran in the coming days, meaning the real question is how much of this is already priced in." The S&P 500 rose 0.9% last week, marking its eighth consecutive weekly gain and its longest weekly winning streak since late 2023. The Dow gained 2.1%, achieving its third weekly increase in four weeks. The Nasdaq Composite rose 0.5% last week, its seventh gain in the past eight weeks. Adam Parker, founder of Trivariate Research, wrote, "There's no question fundamentals are at least part of the reason for this market rally. Earnings are expected to grow 23% this year and 16% next year, so there is a credible argument that forward P/Es are actually contracting modestly despite rising earnings expectations and strong earnings growth." Falling oil prices also boosted equities last week. U.S. crude fell 8.4% last week, its largest weekly decline since April 17. However, with oil prices still significantly higher than earlier this year and price pressures remaining elevated, investor expectations for Federal Reserve policy easing have cooled. In fact, according to the CME FedWatch Tool, traders now see an 8.5% probability of a rate hike in July, up from 0.9% a month ago.