The Israeli military said it called up reservists and was imposing a total blockade of the Gaza Strip in signs it could be planning a ground assault there to defeat Hamas which launched a deadly attack over the weekend.

But late in the afternoon, a senior Hamas official said the group is open to discussions over a possible truce with Israel. U.S. President Joe Biden said he directed his team to coordinate with regional partners to warn anyone seeking to take advantage of the situation.

News of the conflict sparked an oil rally due to supply concerns. But stock indexes managed to reverse earlier declines with help of more dovish Federal Reserve official comments.

As a result investors appeared to refocus on more U.S. centric matters, John Augustine, said chief investment officer at Huntington National Bank in Columbus, Ohio.

"The stock market and investors are focused on two things, the economy and earnings. The U.S. economy is not slowing and earnings are expected to come out of a recession with reports starting this week," Augustine said.

"Those fundamentals are more powerful in the market than terrible geopolitical headlines from the weekend just as they were more powerful than a strong jobs report and worries about the Fed on Friday."

The U.S. bond market was shut on Monday for Columbus Day, also known as Indigenous Peoples' Day.

A recent surge in U.S. Treasury yields had pressured equities. That pressure eased as gains in the iShares Core 10+ years U.S. bond Exchange Traded Fund (ETF> and the iShares 20+ years Treasury bond ETF suggested that yields could fall on Tuesday.

Meanwhile, Fed officials indicated that recent gains in yields on long-term U.S. Treasury bonds, which directly influence financing costs for households and businesses, could steer the Fed from further hikes in its short-term policy rate. This eased some concerns among equity investors.

According to preliminary data, the S&P 500 gained 27.35 points, or 0.63%, to end at 4,335.85 points, while the Nasdaq Composite gained 53.90 points, or 0.40%, to 13,485.24. The Dow Jones Industrial Average rose 199.83 points, or 0.60%, to 33,607.41.

Traditional safe-haven assets remained in demand, with gold climbing, but the U.S. dollar index gave up earlier gains.

Rising oil prices boosted the S&P energy sector, making it the biggest gainer among the S&P 500's 11 major industry sectors.

United Airlines, Delta Air Lines and American Airlines suspended direct flights to Tel Aviv. Shares of the airlines, also hurt by rising oil prices, putting pressure on the S&P 500 Passenger Airlines index.

Defense companies had rallied after the news from Israel, with the S&P 500 Aerospace & Defense index. Big advancers included Northrop Grumman and L3Harris Technologies.

Exchange-traded funds exposed to Israel were selling off, with iShares MSCI Israel ETF falling along with the ARK Israel Innovative Technology ETF.