Stocks were mixed on Tuesday amid renewed tensions in the Persian Gulf, although investors also clung to hopes of a deal between the U.S. and Iran to end the war.

The U.S. military overnight struck Iranian missile launch sites and other targets, attacks that Iran's Foreign Ministry called a "grave violation" of the countries' ceasefire. President Trump said on Saturday that a peace agreement had been "largely negotiated."

The S&P 500 rose 46 points, or 0.6%, to 7,519 on Tuesday. The Dow Jones Industrial Average slipped 118 points, or 0.25%, to 50,462. The tech-heavy Nasdaq jumped 1.2%.

Benchmark U.S. crude oil declined $2.92, or 3%, to $93.68 a barrel. Brent crude, the international standard, gained $3.50, or 3.6%, to $99.67 a barrel. 

Stocks have climbed to new records despite the jump in oil prices since the Iran war began in late February, buoyed by hopes that the conflict will be short-lived. But higher oil prices have pushed up gasoline and other energy costs, driving inflation to its highest level in almost three years and squeezing household budgets.

"At this point in time, formally ending hostilities and reopening Hormuz is nothing but positive," said Adam Crisafulli, an analyst at Vital Knowledge, in a Tuesday research note. "Stocks have been on a multi-week tear, and while anticipation of an Iran détente certainly played a role, there was still a fair degree of anxiety in the market that the U.S. and Israel would resume air strikes, kicking off a catastrophic spiral of violence that would have dramatically exacerbated the existing energy/supply chain strains."

Average gasoline prices have eased in recent days, also on optimism that the two nations will reach an accord. National Economic Council Director Kevin Hassett told Fox Business that he believes "energy prices are going to plummet" once the Strait of Hormuz reopens to oil tanker traffic.

"Average gasoline prices declined in 40 states over the last week as falling oil prices helped offset earlier price cycling in many markets, bringing relief to motorists after several states had already seen sharp increases," Patrick De Haan, head of petroleum analysis at GasBuddy, said in a Tuesday research note.

The average price for a gallon of gasoline stood at $4.49 on Tuesday, down from $4.53 a week earlier, according to AAA.

U.S. markets were closed on Monday for the Memorial Day holiday. On Friday, the S&P 500 added 0.4%, and the Dow industrials climbed 0.6%. The Nasdaq composite gained 0.2%.

Global markets advanced Monday after regional officials in the Middle East said the United States was close to reaching an agreement with Iran to end the war, reopen the Strait of Hormuz and see Iran give up its stockpile of highly enriched uranium. But it's not clear when or how the deal might be finalized and when its various parts will take effect.

An end to the war would ease concerns throughout a region that saw Gulf havens and travel hubs like the United Arab Emirates struck by Iranian missiles and drones. 

It would allow for global shipping, including an estimated 20% of the world's oil, to resume flowing through the Strait of Hormuz. It would also allow the rebuilding of energy and other infrastructure in the region.

"Markets increasingly believe economic pressure will force diplomacy to move faster than military escalation," said Nigel Green, CEO of the investment firm deVere Group, in an email. "Washington can project strength militarily, but sustained triple-digit oil creates economic consequences the US simply cannot ignore."