Treasury yields fell Friday after the U.S. government said the economy added far fewer jobs than expected during the month of May.

At around 8:48 a.m. ET, the yield on the benchmark 10-year Treasury note, which moves inversely to price, was lower at 2.055%, while the yield on the 30-year Treasury bond was down to around 2.571%.

The 2-year Treasury note, which closely reflects Fed policy, was yielding 1.779% Friday morning, well off the 2.25% it reached in late May.

The Labor Department's report showed that job creation slowed in May, with nonfarm payrolls up just 75,000 even as the unemployment rate remained at a 50-year low. The decline was the second time in four months that payrolls increased by less than 100,000 as the labor market continues to show signs of reaching maximum employment and weaker month-over-month gains. Economists polled by Dow Jones had expected 180,000 jobs.

"It was a weak number overall, and people are scratching their heads, but it's in line with what ADP showed us," said Arthur Bass, managing director of fixed income financing, futures, and rates at Wedbush Securities. "I don't think it puts June on the table. ... I think it's all going to depend on the trade stuff."

Market expectations for a Fed rate cut in June rose to 27.5% from 16.7% after the data release, according to the CME Group's FedWatch tool. The market is also pricing in a 79% chance of lower Fed rates by July.

In addition to the anemic May numnbers, the prior two months' reports saw significant downward revisions with March's count corrected to 153,000 from 189,000. April's number was cut to 224,000 from 263,000.

Wage growth, often viewed by fixed-income traders as an early inflation predictor, also slowed a bit. Average hourly earnings year over year were up to 3.1%, one-tenth of a point lower than expectations.

On Wednesday, ADP's May payroll report, often seen as a precursor to the government report, came in at a remarkably low 27,000 private sector payrolls added in May but was seen as an anomaly.

A number of economists changed their forecasts over the past week to price in two rate cuts from the Fed this year. This came after President Donald Trump's threat to impose tariffs on all Mexican goods, sending the stock market into volatile territory and causing the bond market to price in a lower rate environment.

— CNBC's Patti Domm contributed to this report.