* Traders focus on weak details in June jobs report
* U.S. to sell $61 bln coupon-bearing debt this week
* Fed to buy $1.00-$1.25 bln bonds due 2036-2044
* Fed to offer 7-day term deposit at 0.30 percent
NEW YORK, July 7 (Reuters) - Longer-dated U.S. Treasuries yields slipped on Monday on buying supported by the view 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 concluded the labor market still has plenty of slack with the historically low worker participation rate and a slow rate of wage growth that will hold back any pickup in consumer spending.
"It wasn't as good as the numbers first looked," said Larry Milstein, head of government and agency trading at R.W. Pressprich & Co. in New York.
This labor backdrop together with relatively muted inflation should allow Fed policy-makers to leave U.S. short-term rates near zero at least into the second half of 2015, analysts said.
Benchmark Treasuries yields initially 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.
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 2.634 percent, over 1 basis point from late on Thursday when it traded as high as 2.692 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 0.520 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," Milstein said.
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 will buy $1.00 billion to $1.25 billion in Treasuries due in 2036 to 2044 at 11 a.m. (1500 GMT).
It will also offer banks to seven-day term deposits at an interest rate of 0.30 percent. This policy tool is aimed to reduce reserves from the banking system when the Fed decides to tighten policy.
(Reporting by Richard Leong; Editing by Chizu Nomiyama)