The Dow climbed sixth-tenths of a percent, the S&P 500 gained a quarter of a percent and the Nasdaq added two-tenths of a percent.

Investors will see if inflation is continuing to moderate when the Consumer Price Index report for June is released on Wednesday. That could shed light on the interest rate outlook, with many traders expecting the Federal Reserve to raise rates by 25 basis points this month after pausing in June.

Philip Palumbo, CEO and Chief Investment Officer of Palumbo Wealth Management, believes more rate hikes are necessary but will lead to some pain for the economy.

"Inflation is no doubt decelerating, and that's a great thing for overall consumers, but everybody has to remember that the Fed looks at core PCE, which takes away food and energy, which are more volatile. [FLASH] So what the Fed needs to do, is they need to continue to put their foot on the gas pedal to get the economy to a point where we go into a recession. They don't want to say that, but that's ultimately what's going to happen."

S&P 500 company earnings unofficially kick off this week with reports from big U.S. banks. Data from Refinitiv showed that analysts expect earnings to have fallen 6.4% in the second quarter compared to a year ago.

In company news, shares of chip maker Intel rose nearly 3% while rival Qualcomm's rose 1% after U.S. Treasury Secretary Janet Yellen said over the weekend that meetings with senior Chinese officials were "direct" and "productive."

And shares of Icahn Enterprises surged more than 20% after the investment firm said its founder - 87-year-old billionaire Carl Icahn - and banks have finalized amended loan agreements that untie the legendary activist investor's personal loans from the trading price of his firm.