The S&P 500 finished Tuesday's session near the flatline as the benchmark once again failed to refresh its all-time high from May.

The broad equity benchmark rose less than 1 point to 4,227.26, sitting 0.3% below its record high of 4,238.04 reached on May 7. The Dow Jones Industrial Average dipped 30.42 points, or 0.1%, to 34,599.82, while the tech-heavy Nasdaq Composite gained 0.3% to 13,924.91.

Tesla erased earlier gains and fell nearly 0.3% even after an increase in deliveries. The electric car maker delivered 33,463 China-made vehicles in that market in May, a 29% jump from April.

Airline stocks turned higher after the Centers for Disease Control and Prevention eased travel recommendations for 61 countries, including Japan, France, South Africa, Canada, Spain and Italy. United Airlines climbed nearly 0.8%, while Delta jumped about 2.1%. An upgrade from Jefferies on optimism about international and business travel also boosted Delta shares.

Boeing shares gained slightly after Southwest Airlines said it is upsizing its order for the smallest 737 Max model by nearly three dozen planes amid an improvement in travel demand.

The Reddit-fueled trading mania seemed to have spread to other stocks, notably Clover Health and Wendy's on Tuesday. The health care start-up soared as much as 100% and closed the day up about 86%, while shares of the fast food chain rallied 25.8%.

The U.S. Securities and Exchange Commission said Monday it's watching ongoing volatility in the market and vowed to protect retail investors.

On the data front, job openings in April soared to a new record high, with 9.3 million vacancies coming amid the economic recovery. The standard set in April was well above the 8.3 million in March that itself was a new series high going back to 2000 for the Labor Department's Job Openings and Labor Turnover Survey.

"This recent surge in openings suggests that firms are having a hard time filling positions, and the number of quits reported in the JOLTS data also has surged largely, suggesting workers are able to find—or confident in their abilities to find—new positions," JPMorgan strategist Daniel Silver, said in a note. "Both of these factors signal a need for firms to raise wages, and we have seen a variety of related measures pick up lately."

Elsewhere, multiple global websites were experiencing an outage early Tuesday, but the size of the issue and how widespread it is was unclear. Futures, especially those for the tech-heavy Nasdaq, had appeared to take a leg down when news of the outage spread, but then quickly recovered most of those losses. It was unclear at this point if the move was related.

May's consumer price index is set to be released Thursday. Economists are expecting the CPI to rise 4.7% from a year earlier, according to Dow Jones. In April, the CPI increased 4.2% on an annual basis, the fastest rise since 2008.

All eyes are on the next Federal Open Market Committee meeting scheduled for June 15 and 16 as investors look for what central bank officials will say about inflation and monetary policy. Recent comments by officials suggest the Fed is beginning to prepare markets for tapering its asset purchases.