July 15 (Reuters) - U.S. economic activity increased slightly in recent weeks, employment rose, and companies and households indicated that inflation may have improved, the Federal Reserve said on Wednesday, in a report that will help shape the policy debate when Kevin Warsh leads his second interest rate-setting meeting in two weeks.

"Contacts generally expected the economy to continue to expand in the coming months, but several districts noted elevated uncertainty in the outlook for fuel costs," the Fed said in its latest "Beige Book" report, which collects qualitative economic data from all 12 of its regional banks to give policymakers a real-time read on current conditions.

"Compared with the last reporting period, price growth was the same or slower in all Districts," it said. "Expectations for price growth over the coming months varied across districts, with contacts in some expecting inflation to continue at its current pace, while contacts in others expected inflation to slow, in part due to falling fuel prices."

Elevated inflation, which Fed policymakers say stems from last year's tariff increases, higher oil prices since the start of the war in the Middle East, and AI-driven investment, pushed about half of the central bank's policymakers at the June 16-17 meeting to project at least one rate hike by the end of 2026.

A drop in fuel prices last month due to a preliminary peace agreement between the U.S. and Iran helped cool inflation, data this week showed, but renewed hostilities this month have pushed oil prices back up and reignited inflation concerns.

Warsh has repeatedly promised to restore price stability and said the central bank has the tools to do so, something he reiterated in back-to-back appearances before lawmakers in Congress on Tuesday and Wednesday.

He has also declined to say whether he feels rate hikes will be required, keeping to his longstanding view that forward guidance on the outlook for rates does more harm than good.