June 21 (Reuters) - U.S. Treasury yields wavered in quiet trade on Friday, slipping early in tandem with European yields then ticking up to just above flat after a surprisingly strong business activity report indicated that the Federal Reserve has another reason to hold off easing interest rates.

Since last Friday, the benchmark 10-year yield has risen 4.1 basis points, the first weekly gain in three, while the two-year's yield gained 4 basis points in the first weekly gain in a month.

S&P Global said on Friday that its

flash U.S. Composite PMI

Output Index, which tracks the manufacturing and services sectors, nudged up to 54.6 this month. That was the highest level since April 2022 and followed a final reading of 54.5 in May. The individual indexes on manufacturing and services were both well above expectations and last month's levels, suggesting that the economy ended the second quarter on a solid note.

But other May data this week paint a different picture. Retail sales barely rose after falling in April, and housing starts hit the lowest level in nearly four years.

Unemployment claims data also pointed to an economy that is coming off the boil, all of which is good news for the Fed as it manages inflation that has yet to fall back to the range of its 2% target.

Brian Rehling, head of global fixed income strategy at Wells Fargo Investment Institute, said the benchmark 10-year yield was in a broad trading range between 4.70% and 3.80%, roughly the highs of April and lows of December. "The market is kind of waiting to see which way this thing breaks."

"If the consumer remains resilient, the job market hangs in there, the equity market hangs in there, the Fed delays, then rates probably are going higher from here," Rehling said. But he warned that, "If things start to break and the Fed steps in, then things probably are going lower.

Rehling said the market was focused on Fed speakers. So did Gennadiy Goldberg, head U.S. rates strategist at TD Securities, who said next Friday's Personal Consumption Expenditures Price Index release was probably the main upcoming event for the market, as it is the Fed's favorite inflation gauge.

Also high on the watch list is next week's auction of about $183 billion in U.S. two-, five- and seven-year Treasury notes.

A drop in

euro-zone government bond yields pressured U.S. yields earlier on Friday, after economic survey data came in weaker than expected, supporting expectations for policy rate cuts.

Weak demand dragged down France's business activity as the country heads into a snap parliamentary election, while an upturn in Germany slowed in June.

"You've seen a bit of a risk-off move in Europe with weaker French PMI data. That pushed French yields lower but pushed Germany a lot lower," Goldberg said.

The yield on benchmark U.S. 10-year notes was last up 0.3 basis point from late Thursday at 4.257%. The 30-year bond yield rose 0.4 bp to 4.3971% and the 2-year note yield, which typically moves in step with interest rate expectations, rose 0.1 bp to 4.7301%.

The U.S. Treasury yield curve measuring the gap between yields on two- and 10-year Treasury notes, seen as a barometer of future economic growth, was at a negative 47.5 basis points, little changed from late Thursday.

Fed funds futures suggest the probability of a Fed ease in September is 66%, a bit more than late Thursday, according to LSEG's calculations. Traders are pricing in one to two rate cuts of 25 bps each this year.

(Reporting by Alden Bentley; Editing by Chizu Nomiyama and Leslie Adler)