US 30-year, 10-year and 2-year yields all fell to two-week lows.
"Today's moves were due to weak European data, although we're slowly drifting off the lows in yields so markets are not taking it too badly," said Gennadiy Goldberg, senior rates strategist at TD Securities in New York.
German private sector activity contracted for the first time in 6-1/2 years in September as a manufacturing recession deepened unexpectedly and growth in the service sector lost momentum, a survey showed on Monday.
French business activity also slowed unexpectedly and Markit's euro zone composite flash PMI fell to 50.4 in September from 51.9 in August.
The weak data pushed Germany's benchmark 10-year bond yield to -0.59%, its lowest since the Sept. 12 European Central Bank meeting that concluded with rate cuts and fresh asset purchases to boost weak growth.
In the United States, the IHS Markit manufacturing index for September was 51, slightly better than the consensus forecast and the August number. The US services sector index, on the other hand, was slightly lower than market expectations.
"The mix of (US) data is much better than those out of Germany and the euro zone in general and reflects an economy still in expansion with low inflation, which will keep the October Federal Reserve policy decision on the fence for now," Action Economics said in its blog after release of the numbers.
In morning trading, US benchmark 10-year note yields fell to 1.678% from 1.753% late on Friday, after hitting a two-week low of 1.677%.
Yields on 30-year bonds were also lower, at 2.126% from 2.198% on Friday, touching a two-week trough of 2.12%.
On the short end of the curve, US 2-year yields were down at 1.644% from Friday's 1.712%, after earlier falling to a two-week low of 1.64%.
Andy Catalan, senior portfolio manager and head of long duration at Insight Investment in New York, believes that given generally solid US economic fundamentals, US yields should be higher than where they are currently.
"If you go 12 months out, you would expect the 10-year (yield) to hover around 2 pct," Catalan said. "But we also recognize that from a technical perspective, where there is pressure of lower rates around the world, that it's also pressuring US rates lower despite the prospects that we have here, which are materially different than in Europe."