(Updates prices, adds stock market moves) By Chuck Mikolajczak NEW YORK, July 8 (Reuters) - U.S. government bonds yields continued their recent decline on Thursday, with 10-year Treasury yields touching their lowest levels in nearly five months as investors" worries persist that the best part of the economic recovery may be over. The yield on the 10-year note is on pace to decline for an eighth straight session, marking the longest streak since a nine-session drop that ended on March 3, 2020, as the COVID-19 pandemic in the United States was gaining speed. Recent data on the labor market and services sector has given investors pause that the economy may not be strengthening as initially anticipated and some underlying weakness may be emerging. On Thursday, initial jobless claims unexpectedly rose for the week, according to Labor Department data, although the broader trend continues to show improvement. A closely watched part of the U.S. Treasury yield curve measuring the gap between yields on two- and 10-year Treasury notes, seen as an indicator of economic expectations, was at 108.9 basis points after flattening to as small as 104.2, the most narrow since Feb. 12. "There is a little bit of a preoccupation on the employment front where the market is questioning if the Fed will be able to make further progress on employment in order to meet its mandate before tapering asset purchases," said Subadra Rajappa, head of U.S. rates strategy at Societe Generale In New York. "The market is pricing out the timing of the first rate hike, as well as the pace of rate hikes after the first rate hike, and that led to this flattening move in Treasuries." Minutes from the Fed"s June 15-16 meeting showed central bank officials believed "substantial further progress" on the economic recovery had not yet been met, but agreed they needed to be prepared to act should inflation or other risks emerge. Analysts have cited multiple reasons for growing concerns about the economic growth prospects and increasing risk-off sentiment, including the Delta variant of COVID-19, volatility in oil prices and a market that has been largely positioned short. The yield on 10-year Treasury notes was down 3.5 basis points to 1.286% after hitting a low of 1.25%, the lowest since Feb. 16. The concerns also spread to the stock market, where each of the three major averages were lower in a broad sell off, with sectors considered part of the "reflation" trade such as financials and industrials the worst performing on the day. The yield on the 30-year Treasury bond was down 3.4 basis points to 1.910% after dropping to 1.856%, marking its lowest level since Feb. 2. July 8 Thursday 2:46PM New York / 1846 GMT Price US T BONDS SEP1 163-31/32 0-22/32 10YR TNotes SEP1 133-224/256 0-84/256 Price Current Net Yield % Change (bps) Three-month bills 0.0525 0.0532 0.000 Six-month bills 0.05 0.0507 -0.005 Two-year note 99-221/256 0.1944 -0.022 Three-year note 99-176/256 0.3571 -0.040 Five-year note 100-174/256 0.7356 -0.044 Seven-year note 101-80/256 1.0543 -0.039 10-year note 103-32/256 1.2862 -0.035 30-year bond 110-140/256 1.9098 -0.034 DOLLAR SWAP SPREADS Last (bps) Net Change (bps) U.S. 2-year dollar swap 8.00 0.25 spread U.S. 3-year dollar swap 11.75 0.00 spread U.S. 5-year dollar swap 8.00 0.25 spread U.S. 10-year dollar swap -1.25 1.00 spread U.S. 30-year dollar swap -29.25 2.00 spread (Additional reporting by Karen Brettell; Editing by Mark Heinrich and Andrew Heavens)