* U.S. two-year yields drop to three-week lows

* U.S. 10-year yields fall to two-week lows

* U.S. jobs rise to 175,000 in April, lower than forecast

* U.S. services sector contracts in April

* U.S. rate futures price in two cuts of 25 bps this year

NEW YORK, May 3 (Reuters) - U.S. Treasury yields tumbled to multi-week lows on Friday after data showed the world's largest economy created fewer jobs than expected last month, reinforcing expectations that the Federal Reserve will start cutting interest rates later this year.

The benchmark U.S. 10-year yield fell to a two-week low of 4.453% after the data, and was last down 6.9 basis points (bps) at 4.501%. On the week, the yield was down 16.7 bps, on track for the biggest weekly fall since roughly mid-December.

The two-year yield, which reflects interest rate expectations, slid to three-week troughs of 4.716%, and it was last at 4.809%, down 6.7 bps. With a weekly drop of 19 bps, the two-year yield was on pace for its largest decline since around early January.

Data showed that U.S. nonfarm payrolls rose by 175,000 jobs in April. The jobs number for March was revised higher to show payrolls rising by 315,000 jobs instead of 303,000 as previously reported. Economists polled by Reuters had forecast payrolls advancing by 243,000.

The unemployment rate remained below 4% for the 27th straight month.

"I think the jobs data and jobless number tell us what they have been telling us for quite some time. It's not so much the headline number: It's really about the underlying details," said Jeff Klingelhofer, co-head of investments at Thornburg Investment Management in Santa Fe, New Mexico.

"When you look at temporary workers coming down, when you look at full-time employment versus part-time employment, what we see is that the economy is slowing and the mismatch between labor supply and demand is getting back into relative equilibrium," he added.

The jobs report was followed by data showing the U.S. service sector contracted in April, while price pressures jumped. The Institute for Supply Management (ISM) said its non-manufacturing PMI fell to 49.4 last month from 51.4 in March, the lowest since December 2022. A reading above 50 indicates growth in the services industry, which accounts for more than two-thirds of the economy.

Services inflation has picked up, with the measure of prices paid for inputs by businesses jumping to 59.2 from 53.4 in March.

Following the jobs report, U.S. rate futures priced in two cuts of 25 basis points (bps) for 2024, most likely starting in September or November, according to LSEG's rate probability app. For the last few weeks, the futures market had factored in just one cut on the back of still-elevated inflation.

Fed Governor Michelle Bowman said on Friday she expects inflation to decline further with a steady policy rate, but she still sees upside inflation risks that may affect her outlook.

Bowman also said she remains willing to raise the fed funds rate at a future meeting if data showed inflation has stalled or reversed.

In other maturities, the U.S. five-year yield sank to a three-week low of 4.41% and was last at 4.488%, down 7.8 bps.

On the long end of the curve, U.S. 30-year bond yields sagged to a more than one-week trough of 4.633% and were last down 5.2 bps at 4.665%.

The U.S. yield curve, meanwhile, modestly steepened or narrowed its inversion. The spread between U.S. two- and 10-year yields tightened to minus 26.5 bps, after the jobs number, from minus 29.6 bps late on Thursday. It was last at minus 28.9 bps.

This curve is effectively a "bull steepener," a scenario in which short-term interest rates are falling faster than the long-dated ones. This suggests that the Fed's next move is a rate cut.

"Treasury yields will remain within a broad trading range for the next few months, capped by last October's cyclical peak on the upside and the lows seen earlier this year (roughly 3.80% on the 10-year) on the downside," wrote Ryan Swift, U..S bond strategist, at BCA Research in Montreal.

"Ultimately, yields will break out to the downside of this range, but we will need to see more weakness in the labor market data before that occurs."

(Reporting by Gertrude Chavez-Dreyfuss; Editing by Nick Zieminski and Jonathan Oatis)