* Traders focus on weak details in June jobs report
* Some economists now see earlier Fed rate hike
* U.S. to sell $61 bln coupon-bearing debt this week
* Fed buys $2.774 bln Treasuries due 2021-2024
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NEW YORK, July 7 (Reuters) - Longer-dated U.S. Treasuries yields fell on Monday on buying supported by the view that the recent acceleration in job gains is not enough to spur the Federal Reserve to raise short-term interest rates earlier than expected.
While Thursday's government payrolls report showed a robust 288,000 increase in hiring in June and the jobless rate fell to a six-year low at 6.1 percent, some traders were not convinced the labor market is strong enough for Fed Chair Janet Yellen and other policymakers to tighten policy sooner. The historically low worker participation rate and a slow rate of wage growth will likely restrain consumer spending, which accounts for two-thirds of the U.S. economy.
"The data haven't been strong enough to change Yellen's approach," said Jason Rogan, managing director of Treasuries trading at Guggenheim Partners in New York.
This labor backdrop together with relatively muted inflation should allow Fed policymakers to leave U.S. short-term rates near zero at least into the second half of 2015, analysts said.
Benchmark Treasuries yields initially had jumped to two-month peaks early Thursday on the June jobs data before ending the session mildly higher on doubts whether the Fed would push up its timing for a rate hike.
Economists at JPMorgan and Goldman Sachs changed their forecasts for such a move to the third quarter of 2015 from the fourth quarter of 2015 and first quarter of 2016, respectively.
The U.S. bond market was closed on Friday for the U.S. Independence Day holiday.
On the open market, the yield on 10-year Treasuries notes was last at 2.617 percent, 3 basis points lower than Thursday when it traded as high as 2.692 percent.
The 30-year yield ended 4 basis points lower at 3.440 percent.
While overseas demand emerged to help push longer-dated yields lower, shorter-dated yields hovered close to their Thursday's closing levels with two-year yields near their nine-month high at 0.516 percent.
Expected foreign appetite for higher-yielding U.S. bonds, analysts say, should stoke bids for this week's $61 billion worth of fixed-rate Treasuries supply: $27 billion in three-year notes on Tuesday ; $21 billion in 10-year debt on Wednesday and $13 billion in 30-year bonds on Thursday.
"This will put a cap on how high Treasuries yields will go," said Larry Milstein, head of government and agency trading at R.W. Pressprich & Co in New York.
While it remains uncertain when the Fed will raise interest rates, it is widely expected the Fed will stop its third round of quantitative easing before year-end. On Monday, it bought $2.774 billion of Treasuries due in 2022 to 2024.
(Reporting by Richard Leong; Editing by Chizu Nomiyama and Nick Zieminski)