By Sinéad Carew and Shashwat Chauhan

(Reuters) - Wall Street indexes closed higher on Tuesday, to notch their third straight day of gains, after dovish comments from U.S. Federal Reserve officials pushed Treasury yields lower as investors cautiously monitored developments in the Middle East.

Following comments from top Fed officials on Monday, Atlanta Fed President Raphael Bostic said the U.S. central bank does not need to raise interest rates any further, and that he sees no recession ahead.

Israeli air strikes attacked Gaza on Tuesday, razing entire districts in the densely populated and impoverished enclave, filling morgues with Palestinians, including women and children, as it took "revenge" for a deadly weekend of Hamas attacks that triggered some of the worst blood-letting in 75 years.

"Everybody has one eye on the Middle East conflict and one eye on what's happening with bond yields. The decline in bond yields is the key driver today," said John Praveen, managing director & co-chief investment officer at Paleo Leon.

While the Fed's dovish comments were helping stocks on Tuesday and investors were being sanguine about the Middle East, Praveen said that view could change if for example the fighting spread to other countries in the region.

Peter Tuz, president of Chase Investment Counsel in Charlottesville, Virginia, also attributed the stock market's gains on Tuesday to declining bond yields even as he said "the level of risk in the world has gone up considerably."

"The action yesterday and today, given what's happened in Israel, has really surprised me. But the flight to safety has made Treasury yields fall enough to push up equities," Tuz said.

Ten of the S&P 500's 11 major sectors advanced with utilities leading gains, while the biggest laggard was energy down 0.02% after its 3.5% rally on Monday.

Late on Tuesday, Minneapolis Federal Reserve Bank President Neel Kashkari said he believes the U.S. economy is on track for a soft landing in which inflation falls back to the Fed's 2% goal but the unemployment rate does not rise sharply.

But while Kashkari said recent gains in Treasury yields could reduce the need for more rate hikes he cautioned that if yields are higher due to changing expectations about Fed policy, it might "need to follow through" to maintain those yields.

Fed Governor Christopher Waller reiterated the U.S. central bank's determination to reduce inflation to its 2% target.

Traders put the chance of interest rates remaining unchanged in November and December at around 86% and 73%, respectively, according to CME's FedWatch tool.

Later in the week, investor focus will turn to inflation data, including September producer and consumer prices as well as the Fed's September meeting minutes. Friday is when third-quarter earnings season kicks off in earnest.

Advancing issues outnumbered declining ones on the NYSE by a 3.08-to-1 ratio; on Nasdaq, a 2.12-to-1 ratio favored advancers.

The S&P 500 posted 11 new 52-week highs and 2 new lows; the Nasdaq Composite recorded 51 new highs and 178 new lows.

On U.S. exchanges 9.91 billion shares changed hands compared with the 10.70 billion moving average from the last 20 sessions.