Treasury bonds pulled back Thursday as an upbeat U.S. service industry report and higher stocks sapped demand for safe assets. The factors trumped disappointing U.S. private-sector jobs data and interest-rate cuts from the European Central Bank which had propped up bond prices earlier in the session.

Focus now shifts to Friday’s non-farm jobs report, one of the key economic data points the Federal Reserve closely monitors in setting monetary policy. Traders said a strong jobs report could spark more selling in Treasury bonds as it could raise anxiety that the Fed could raise official interest rates sooner than investors expect.

“There are investors out there who are still willing to sell U.S. Treasurys despite what is happening in Europe because the fundamentals here are so much better,” said Anthony Cronin, a Treasury bond trader at Société Générale SA. “The ECB just eased, but the Fed is talking about raising interest rates.”

In recent trading, the benchmark 10-year note was 11/32 lower, yielding 2.451%, according to Tradeweb. Yields rise as prices fall.

Despite Thursday’s rise, the yield is near the lowest level since June 2013. The yield was about 3% at the start of the year.

Thursday’s report showed the nonmanufacturing purchasing managers index from the Institute for Supply Management increased to 59.6 in August, the highest since the revised survey’s inception in January 2008.

The ISM’s gauge of manufacturing earlier this week also hit the strongest level since March 2011.

Over the past few months, better U.S. data have failed to push up Treasury yields sustainably. Instead, yields have fallen as foreign investors are attracted by superior yields in the U.S. compared to those in Germany and Japan. A stronger dollar–the euro tumbled Thursday to its lowest level in more than a year–added to the allure of U.S. bonds.

“It is a globalized market and U.S. bonds offer better relative value,” said John Canavan, market analyst at Stone and McCarthy Research Associates in Princeton, N.J.

U.S. bonds had risen earlier after the ECB unexpectedly lowered all its interest rates Thursday and announced two new programs under which it will buy asset-backed securities and covered bonds issued by eurozone banks.

Speaking in a news conference, ECB President Mario Draghi said policy makers are unanimously committed to using additional unconventional measures if needed.

“We are still in a world of zero interest rates and the wall of money is staggering,” said Charles Comiskey, head of Treasury trading at Bank of Nova Scotia in New York. “The ECB just added more liquidity to the system, propping up stocks and keeping bond yields low.”

An additional boost for Treasury bond prices earlier was a report showing 204,000 new jobs in August were added to the private sector, slightly below 215,000 forecast by economists.

Bond investors now set their eyes on Friday’s employment release, a broader gauge of the labor market. Economists expected 225,000 new jobs were added to the economy last month, following a gain of 209,000 in July.

Stone and McCarthy’s Mr. Canavan said a strong report Friday would send bond yields higher but he doesn’t expect it to be a turning point to send yields sustainably higher.

“For U.S. bond yields to rise significantly, we need to see consistent wage inflation picking up speed or rising inflation expectations,” said Mr. Canavan. “So far wage inflation has been non existent,” which allows the Fed to take its time in raising interest rates, therefore keeping a lid on bond yields’ rise.

Fed Chairwoman Janet Yellen has signaled in recent months that the central bank is not in a rush to raise interest rates as long as wage inflation remains contained, even as many other indicators have shown the U.S. economy picking up speed from the winter doldrums.