Fears of an economic slowdown in Europe were exacerbated after the U.S. government on Monday threatened to impose tariffs on $4 billion of additional euro zone goods in a long-running dispute over aircraft subsidies.

The yield on the benchmark 10-year Treasury note was 6 basis points lower at around 1.977%. The yield's move back above 2% this month after China and the U.S. agreed to a trade deal ceasefire proved to be short lived. The yield on the 10-year bund fell to -0.367% in afternoon trading in Germany. Bond yields move inversely to their prices.

The 10-year Treasury yield fell back under 2% on Tuesday as concerns about global economic growth pushed investors toward safer assets. In Europe, the benchmark German bund yield fell to a new record low.

The U.S. Trade Representative's office released a list of products — including Italian cheese, olives and whiskey — that could be targeted with new duties on top of those implemented in April. The new wave of proposed duties comes amid a 15-year dispute at the World Trade Organization over aircraft subsidies given to U.S. aerospace manufacturer Boeing and its European rival, Airbus.

Those trade concerns have weighed on an already-dampened global growth outlook, with European rates falling across the board during Tuesday's session. That's prompted both Federal Reserve and European Central Bank officials to curb talk of tighter monetary policy and suggest easier conditions later in the year.

Speaking in London, Cleveland Fed President Loretta Mester said Tuesday that the Fed can hold steady on interest rates while waiting for economic data points to emerge.

"At the present time, I believe it is too soon to make that determination, and I prefer to gather more information before considering a change in our monetary policy stance," Mester said, noting that the expansion has proven "resilient to a variety of shocks, headwinds and uncertainties" that ultimately have reversed.

"A combination of falling global PMIs that suggest lower growth and inflation dynamics going forward and a seemingly willing ECB to engage in further rate cuts and QE is pushing yields lower and further negative," Jim Caron, managing director of Global Fixed Income at Morgan Stanley Investment Management, said in an email.

"Add all this to global central banks cutting rates and it makes sense why bund yields have fallen. It may beg the question, why haven't the fallen even more!" he added.

— CNBC's Jeff Cox contributed reporting.