Stocks on Wall Street edged higher Tuesday amid growing hopes the Federal Reserve is done with interest rate hikes for now but with investors still cautious as the Middle East conflict escalated.

The Dow Jones Industrial Average (^DJI) closed up around 0.4%, while the S&P 500 (^GSPC) gained 0.5%. The tech-heavy Nasdaq Composite (^IXIC) also added roughly 0.6%, after the stock indexes reversed losses to close higher on Monday.

As stocks climbed higher, Treasury yields continued to fall with the yield on the 10-year (^TNX) falling 16 basis points to trade near 4.63% amid a wider sell-off in bonds.

The gains came after dovish comments from two Fed officials, who signaled that the recent surge in bond yields could lead to the tightening in credit conditions the central bank is looking for. That could give policymakers a reason to call an end to raising rates in this cycle, some analysts believe.

The latest was Atlanta Fed President Raphael Bostic, who said Tuesday he believes current rates are high enough to get inflation back to the Fed's 2% target.

Read more: What the Fed rate-hike pause means for bank accounts, CDs, loans, and credit cards

But the IMF has warned that monetary policy needs to remain tight in most places, as central banks are "not quite there" on bringing tenacious inflation down toward targets.

Easing some pressure on stocks, Treasury yields dropped as trading reopened on Tuesday after closing for a holiday. The 10-year Treasury (^TNX) yield came off its 16-year peak even as investors kept watch on the clashes between Islamist militant group Hamas and Israel, which has vowed to put the Gaza strip under siege.

In another sign of easing worries, oil prices fell after gaining more than 4% as investors eyed potential supply disruptions from the Middle East conflict. Crude oil futures (CL=F) and Brent crude futures (BZ=F) both lost almost 1% to trade just below $86 and above $87, respectively.

In individual stocks, PepsiCo (PEP) shares rose almost 2% after the maker of Pepsi soda and Frito Lay snacks hammered Wall Street estimates for third quarter profit and raised its annual earnings forecast.

Click here for the latest stock market news and in-depth analysis, including events that move stocks

Read the latest financial and business news from Yahoo Finance