* Exxon posted record second-quarter diesel output

* Chevron's ( CVX ) US refineries processed a record of more than 1

million barrels daily

* Exxon CEO says refining challenges will remain for a while

By Sheila Dang

HOUSTON, July 31 (Reuters) - Top U.S. oil producers

ExxonMobil ( XOM ) and Chevron ( CVX ) warn that global supplies

of diesel and other refined products will likely remain tight

and lead to persistently high prices in the second half of the

year as the Iran war continues to cause major energy

disruptions.

Both companies reported large jumps in second-quarter refining

profits on Friday as declining fuel stockpiles combined with

curtailed exports from China and refinery outages inRussia led

to higher margins.

"We're going to see some upward pressure on product pricing

... into the third quarter and perhaps beyond that," Chevron ( CVX ) CEO

Mike Wirth said during an earnings call, adding that demand for

distillates including diesel and heating oil is unlikely to

decline over the long term.

The rising margins and subsequent profits are occurring as U.S.

gasoline prices crossed $4 a gallon again last week, presenting

a political challenge for President Donald Trump and the

Republican Party that will be campaigning to hold onto

majorities in Congress in the November midterm elections. The

biggest U.S. oil majors say they are doing everything they can

to keep output high.

HIGH PRODUCTION

Exxon said it ran its U.S. refineries at high capacity and had a

record second quarter for diesel production, while Chevron ( CVX ) said

it had record throughput at its U.S. refineries of more than 1

million barrels per day.

Still, Exxon CEO Darren Woods said it is critical that

shipping resumes through the Strait of Hormuz to supply more

crude to the market.

"The utilization that we've seen can't be sustained for the

long term. So I think this refining challenge is going to be

with the world for a while," he said on CNBC.

Woods added that the company has the largest refining

footprint in the world outside of China, and the disruption to

crude supplies added difficulties to the downstream business.

Refiners must complete necessary maintenance, and Chevron ( CVX ) said

downtime in the third quarter was expected to hit downstream

earnings by $175 million to $225 million.

Exxon said scheduled maintenance would be lower during the

third quarter compared with the previous three months.

While Exxon's adjusted downstream earnings rose to $4.1

billion, some investors may have expected Exxon to report even

stronger refining results given its large refinery footprint,

RBC Capital Markets analyst Biraj Borkhataria said in a research

note.

Exxon narrowly missed consensus estimates for second-quarter

earnings, while Chevron ( CVX ) surpassed expectations. Exxon shares

were down 1%, while Chevron ( CVX ) was up about 2%.