Wall Street's main indexes closed higher Wednesday as oil prices fell while Iran reviewed a U.S. proposal to end the war in the Middle East, feeding investor hopes for de-escalation in the fourth week of a war that has disrupted global energy flows and stoked inflation concerns.

While Abbas Araqchi, Iran's foreign minister, said top authorities were reviewing proposals, he added that exchanges of messages through mediators do not equate to negotiations and that Tehran has no intention to hold talks with the U.S.

Initially, Iran said it considered U.S. proposals delivered by Pakistan as excessive and demanded sovereignty over the Strait of Hormuz.

With the mixed messages leading to choppy equity trading during the day, Michael James, equity sales trader at Rosenblatt Securities, said: “There are a lot of frayed nerves out there with sentiment and headlines driving a lot of the market action.”

Any signs of communication between the countries made investors hopeful, following signals that Washington has been seeking a ceasefire and restoration of shipping through the crucial Strait of Hormuz, which about 20% of global oil shipments pass through.

"There is optimism that the proposal and counter-proposal are setting the stage for more negotiations," said Gene Goldman, chief investment officer at Cetera Investment Management.

Until there is clarity on when the war might end, Goldman said he expects "volatility to remain elevated given the impact of higher oil prices on inflation."

According to preliminary data, the S&P 500 gained 35.60 points, or 0.54%, to end at 6,591.97 points, while the Nasdaq Composite gained 169.73 points, or 0.77%, to 21,931.62. The Dow Jones Industrial Average rose 306.42 points, or 0.66%, to 46,430.48.

During Wednesday's session, energy was the weakest of the S&P 500's 11 major industry sectors. Strong gainers included materials and consumer discretionary .

With oil prices settling down more than 2%, shares in companies that depend heavily on fuel were rallying. Cruise operators including Norwegian Cruise Line gained sharply along with airlines, with the S&P Composite 1500 Passenger Airlines index outperforming the broader market.

The small-cap Russell 2000 index hit a two-week high during the trading session.

U.S.-listed shares of Arm rallied sharply after the company unveiled a new AI data center chip that is expected to bring billions of dollars in revenue. It was the biggest gainer in the Philadelphia Semiconductor Index. Other rallying chipmakers included Advanced Micro Devices and Intel . Nvidia shares also rose.

Destiny Tech100 surged after a report that SpaceX aims to file its IPO prospectus as soon as this week. SpaceX is the fund's largest equity holding.

Other space companies also rose including Rocket Lab , Intuitive Machines and EchoStar. The oil price spike has revived inflation worries, complicating the interest-rate outlook of central banks.

Markets are no longer pricing in any easing from the Federal Reserve this year, according to CME Group's FedWatch Tool, compared with the two cuts that were expected before the war broke out.

Among other movers, U.S.-listed shares of JD.com and Alibaba rose after Chinese state media and the regulator urged the food-delivery platform industry to end a price war. Robinhood Markets rallied after the trading platform announced a new $1.5 billion share buyback program.