U.S. equities remained relatively unchanged on Tuesday as investors carefully analyzed the latest economic data and comments made by Federal Reserve Chair Jerome Powell regarding potential interest rate cuts. Powell, speaking at the European Central Bank (ECB) forum, expressed optimism about progress made in disinflation and acknowledged a cooling labor market.

Powell's comments reinforced market expectations of reduced borrowing costs later this year. While he did not commit to a specific course of action, he anticipated inflation to be between 2% and 2.5% by next year. Traders are eagerly awaiting the ADP employment report on Wednesday and the official June jobs report on Friday to gather further insights about the labor market.

In other news, Tesla Inc. made headlines as its second-quarter deliveries exceeded market expectations. The electric vehicle giant, led by Elon Musk, delivered 443,956 vehicles in Q2, surpassing estimates of 438,019 vehicles. This news led to a surge in Tesla's stock, rallying over 9% and making it one of the standout performers.

Meanwhile, the Job Openings and Labor Turnover Survey (JOLTS) report revealed a significant increase in job vacancies. In May, there were 8.14 million job openings, surpassing the forecasted 7.91 million. This spike in job openings reflects potential positive momentum in the labor market.

Despite the developments in the stock market and labor market, major U.S. indices and sectors traded within narrow ranges, with little movement observed in commodities. Treasury yields remained mostly unchanged, with the 10-year yield at 4.45%. West Texas Intermediate (WTI) light crude and gold showed minimal fluctuations, trading flat at $83.50 and dipping by 0.3% respectively.

Overall, Tuesday's trading session demonstrated cautious optimism among investors as they interpreted Powell's remarks about disinflation progress and monitored job market indicators. With the ADP employment report and the official June jobs report yet to come, market participants are eagerly awaiting further labor market insights to inform their investment decisions.