NEW YORK (AP) — Financial markets are moving cautiously Thursday, a day after surging on optimism about a ceasefire in the war with Iran, and U.S. stocks are rising even though oil prices are too.

The morning began with modest losses for Wall Street following drops for Asian and European stocks. But the S&P 500 erased its dip and was up by 0.7% in afternoon trading after Israel said it would begin direct negotiations with Lebanon. That helped calm worries that the two-week ceasefire announced late Tuesday could already be in trouble because of Israel's bombardment of Lebanon.

The Dow Jones Industrial Average was up by 382 points, or 0.8%, as of 1:56 p.m. Eastern time, and the Nasdaq composite was 0.8% higher after both indexes likewise recovered from early losses.

Crude oil prices pared some of their gains, but they nevertheless remained higher for the day on continued uncertainty about when oil tankers can start fully flowing through the Strait of Hormuz. The narrow waterway has been at the center of President Donald Trump’s demands of Iran, and blockages there have kept oil and natural gas stuck in the Persian Gulf and away from customers worldwide.

The price for a barrel of benchmark U.S. crude rose 1.4% to $95.78 after briefly nearing $103 in the morning. Brent crude, the international standard, added 0.1% to $94.87 per barrel.

Given how far apart the United States and Iran seem to be in their demands, upward pressure on oil prices may be “here to stay for a while” according to strategists at Macquarie led by Thierry Wizman. Risks remain for renewed fighting, which could cause customers worldwide to hoard whatever oil supplies they do get. That could itself keep oil off the market, much like actual fighting targeting pipelines or oil tankers.

Oil prices have been swinging through sharp and sudden reversals for weeks as hopes rose and fell for the Strait of Hormuz to fully reopen and allow production of oil and natural gas to kick back into gear. Brent oil has gone from roughly $70 per barrel before the war in late February to more than $119 at times.

Despite all those swings, the U.S. stock index at the heart of many 401(k) accounts isn't far from its all-time high. The S&P 500 is just 2.1% below its record set in January.

Constellation Brands climbed 7.2% for one of the index's biggest gains on Thursday after reporting stronger results for the latest quarter than analysts expected. The company, which sells Modelo beer and Robert Mondavi wines, said it saw encouraging trends heading into its new fiscal year. But it pulled its financial forecasts for the following fiscal year because of “limited near-term visibility” and other factors.

CoreWeave rallied 5.4% after announcing an expanded, $21 billion deal with Meta Platforms to provide AI cloud capacity through December 2032. Meta rose 3.4%.

On the losing end of Wall Street was Simply Good Foods, which sank 18.2% after reporting a worse drop in revenue than analysts expected. CEO Joe Scalzo called the results unsatisfactory and said the company behind the Quest and Atkins brands is making immediate changes to turn around its performance.

Mixed reports on the U.S. economy also helped keep Wall Street in check. One said an underlying measure of inflation that the Federal Reserve considers important was slightly hotter in February than economists expected. It decelerated before the war with Iran began, but not by as much as economists expected.

A separate report said that more U.S. workers applied for unemployment benefits last week than economists expected. The number was not very high compared with history, but it could indicate an acceleration in layoffs.

Treasury yields swiveled up and down in the bond market following the reports before falling as oil prices pared their gains.

The yield on the 10-year Treasury fell to 4.27% from 4.29% late Wednesday. It, though, remains well above its 3.97% level from before the war, which has sent rates up for mortgages and other kinds of loans going to U.S. households and businesses.

If oil prices stay high and keep upward pressure on inflation, the Federal Reserve would have difficulty resuming its cuts to interest rates to help the slowing economy, even if the job market weakens. A growing number of Fed officials seem to be considering the possibility of a hike in rates, according to minutes of their latest meeting released on Wednesday.

In stock markets abroad, South Korea’s Kospi fell 1.6%, and Germany’s DAX lost 1.1% for two of the world’s biggest moves.

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AP Writers Chan Ho-him, Matt Ott and Aniruddha Ghosal contributed to this report.