Stocks on Wall Street stabilized on Tuesday amid relatively quiet trading, after a report showed that inflation in the United States was not as bad as economists had feared last month. This came despite continued rises in oil prices amid concerns over potential escalation of tensions between the United States and Iran, and the return of large-scale military confrontations.

The S&P 500 index rose 0.1 percent, recovering part of its 0.8 percent loss in the previous session. The Dow Jones Industrial Average fell about 96 points, or 0.2 percent, as of 9:35 a.m. Eastern Time, while the Nasdaq Composite climbed 0.4 percent, according to the Associated Press.

Stocks received support from a decline in U.S. Treasury yields, following data showing that U.S. consumers paid prices 3.5 percent higher in June compared to a year earlier, for gasoline, food, and a wide range of goods and services.

Although this rate is still above the level preferred by most consumers and policymakers, it came in lower than the inflation rate recorded in May at 4.2 percent, and also below economists' expectations of 3.9 percent for June. The slowdown in inflation may ease pressure on the Federal Reserve, which is considering the path of interest rates in the coming period.

Higher interest rates help curb inflation, but they also slow economic activity and increase borrowing costs, affecting various asset classes and investments.

After the inflation data, traders lowered their expectations of a Federal Reserve rate hike at its next meeting later this month to below 17 percent, compared to about 42 percent the previous day, according to data from the Chicago Mercantile Exchange Group.

The decline in bond yields also boosted housing stocks, as lower yields could help reduce mortgage costs and other loans for households and businesses. Shares of Builder's First Source, a building materials company specializing in countertops and windows, rose 1.9 percent, while homebuilder Lennar climbed 1.5 percent.

A recovery in shares of several major computer chip companies helped support market stability, after they had experienced sharp fluctuations in recent weeks due to concerns over high valuations driven by the wave of optimism around artificial intelligence.

Micron Technology shares rose 4.4 percent, while Nvidia climbed 0.6 percent, after both stocks were among the biggest drags on the S&P 500 in the previous session, falling 4.4 percent and 3.5 percent respectively.

However, inflation risks remain, especially with ongoing tensions in the Middle East and the potential disruption of navigation through the Strait of Hormuz, a vital sea passage for oil tankers from the Persian Gulf to global markets.

Brent crude, the global benchmark for oil, rose an additional 3.5 percent to $86.18 per barrel. This followed a nearly 10 percent jump on Monday, bringing prices back to levels seen before the temporary ceasefire agreement between the United States and Iran in mid-last month.

Investors are focused this week on the corporate earnings season, with major financial institutions reporting second-quarter profits, as companies face pressure to show strong growth to justify the significant stock price increases in recent times.

Bank of America, Citigroup, JPMorgan Chase, Goldman Sachs, and Wells Fargo reported on Tuesday quarterly results that exceeded analysts' expectations, supported by strong trading activity and continued resilience in U.S. consumer spending.

Shares of most of these banks rose after the results; Goldman Sachs gained 4.7 percent, while Wells Fargo fell 1.7 percent.

In contrast, IBM shares were among the biggest losers on Wall Street, weighing on the Dow Jones, after plunging 24.2 percent following CEO Arvind Krishna's remarks that the software and infrastructure segments performed below expectations in the last quarter.

Krishna explained that customers in late June redirected their spending toward servers, storage, and memory, anticipating price increases linked to rising demand for AI technologies. In a letter to investors, he said current conditions require 'perfect execution,' adding that the company did not move quickly enough, and delays in closing several large deals accounted for most of the earnings shortfall.

In the bond market, the yield on the 10-year U.S. Treasury note fell to 4.57 percent, from 4.62 percent at the close of trading on Monday, halting its rise from the 3.97 percent level recorded before the outbreak of war with Iran.

On global markets, European stocks showed mixed performance after a strong session in Asia. Japan's Nikkei 225 index rose 0.7 percent, supported by a 3.3 percent rise in SoftBank Group shares. SoftBank is a major investor in the AI sector; its chairman Masayoshi Son criticized the idea of a bubble in AI-related investments during an event in Tokyo.

Stocks in Shanghai also rose 1.4 percent, after the Chinese government reported that the country's exports rose 27 percent in June compared to last year, supported by strong demand related to AI technologies.