June 3 (Reuters) - U.S. economic activity increased a bit in recent weeks, employment was little changed, and the fallout from higher energy prices due to the war in the Middle East was pervasive, the Federal Reserve said on Wednesday, two weeks before Kevin Warsh convenes his first policy meeting as head of the U.S. central bank.

"Business outlooks for the next six months were reported to have little change in anticipated growth, as elevated uncertainty and signs of weakening consumer spending weighed on sentiment," the Fed said in its latest "Beige Book" report, a roundup of qualitative economic data from across the country that policymakers use to help inform their understanding of the economy and their policy decisions.

"Districts noted that energy-related costs tied to the conflict in the Middle East were the primary driver of inflationary pressures, with spillovers into shipping, packaging, groceries, and fertilizer," it said.

Warsh replaced Jerome Powell as Fed chief in late May just as many central bank policymakers were starting to get more nervous about inflation, which has reaccelerated in recent months, in part due to the U.S.-backed war with Iran. Inflation has been above the Fed's 2% target for more than five years.

The sense within the Fed, based on public comments from policymakers as well as the minutes from its April 28-29 meeting, has shifted away from a shared expectation for an interest rate cut later this year to a growing feeling that a long hold at the current rate setting, or even a hike in borrowing costs, may be in order.

Inflation by the Fed's targeted measure jumped to 3.8% in April from 3.5% in March, while the labor market, which looked to be faltering last year as the Fed cut rates in response, has appeared to stabilize. Economists polled by Reuters expect the unemployment rate to remain at 4.3% when the U.S. government releases its jobs report for May on Friday.

President Donald Trump picked Warsh on the explicit expectation that he would cut rates, but has backed off his demand that it be done immediately due to the recent surge in gasoline prices.

The accounts in the latest Beige Book may add weight to the arguments within the Fed against cutting the policy rate, which the central bank has held in the 3.50%-3.75% range throughout this year.