(Updated at 1040 EDT)

By Karen Brettell

June 5 (Reuters) - Benchmark U.S. 10-year Treasury

yields rebounded from a two-month low on Wednesday but remained

lower on the day after data showed that the U.S. services sector

snapped back into growth mode in May after a short-lived

contraction the month before.

The Institute for Supply Management said its

non-manufacturing purchasing managers index rose to 53.8 last

month from 49.4 in April. The report's business activity index

shot up 10.3 points, the largest rise since March 2021 and

vaulting it to 61.2, the highest level since November 2022.

The business activity index is "really driving that whole

index higher," said Ellis Phifer, managing director of fixed

income research at Raymond James in Memphis, Tennessee.

"It's just a little bit of a fly in the ointment when we're

looking at data that's been coming in a little bit softer than

expected, especially ahead of the nonfarm payrolls coming up on

Friday," he said.

Yields have tumbled this week as softening economic data

boosts expectations that the Federal Reserve will make two 25

basis point cuts this year.

This week's main U.S. economic release will be the

government's nonfarm payrolls report for May due on Friday,

which is expected to show that employers added 185,000 jobs in

May. It comes after April's report showed that jobs growth

slowed more than expected, with 175,000 job gains, the fewest in

six months.

Traders have said that market participants are preparing for

a weaker figure on Friday than economists expect.

Benchmark 10-year yields hit a two-month low after the ADP

Employment report showed earlier on Wednesday that private

payrolls increased by 152,000 jobs last month, below economists'

forecasts for 175,000 in jobs gains.

Benchmark 10-year note yields were last down 2

basis points at 4.314% and got as low as 4.295%, the lowest

since April 1.

Two-year note yields fell 2 basis points to

4.756% and reached 4.741%, the lowest since May 16.

The inversion in the two-year, 10-year yield curve

was little changed on the day at minus 44 basis

points.

This week's bond rally has also been driven by relief over

an absence of new bond supply, after some Treasury auctions last

week saw soft demand.

"This week has really just been about a lack of supply in

the interest rate markets compounding a little bit of negativity

on the economy," said Guy LeBas, chief fixed income strategist

at Janney Montgomery Scott in Philadelphia. "I don't think the

economic downside is enough to explain all the movement."

Other data on Tuesday showed that job openings, a measure of

labor demand, were down 296,000 to 8.059 million on the last day

of April, the lowest level since February 2021.

Personal consumption expenditures (PCE) on Friday showing

that U.S. inflation was steady in April and a report on Monday

showing that U.S. manufacturing slowed for a second straight

month in May added to the bond rally.

Next week's consumer price index (CPI) for May will be key

for guiding Fed expectations in the near-term. It will come on

Wednesday morning before the Fed is due to complete its two-day

policy meeting, when Fed officials will update their economic

and interest rate projections.