U.S. government debt prices rose on Tuesday as investors took cover in safe-haven assets amid a sharp sell-off in equities.

Declines of more than 2 percent in both the S&P 500 and the Dow Jones Industrial Average Tuesday sent investors into the relative safety of government bonds and precious metals like gold. Unease in Europe over Italy's budget proposal also appeared to undercut German and American yields.

At around, 10:21 a.m. ET, the yield on the benchmark 10-year Treasury note fell to 3.117 percent, while the yield on the 30-year Treasury bond fell to 3.317 percent. Bond yields move inversely to prices.

"It's not surprising to see a classic flight-to-quality supporting the Treasury market," Ian Lyngen, head of U.S. rate strategy at BMO Capital Markets, wrote in an emailed statement. "The impetus for the move wasn't entirely technical as the Italian budget issue once again found itself fumbling toward the limelight. With Italy now saying it will be sticking to its spending proposal that doesn't adhere to EU guidelines, the implications are for an unprecedented showdown with Brussels."

The Treasury yields climbed last week amid fears that the Federal Reserve may be hiking interest rates too high, too fast. Minutes released by the U.S. central bank last week from its most recent meeting showed the Fed's continued hawkish view on rates. President Donald Trump has criticized the Fed over its monetary policy stance, going as far as to call the institution "crazy."

But on Tuesday, yields extended losses seen in the previous session, as traders turned their focus to rising political worries surrounding the unexplained death of Saudi journalist Jamal Khashoggi at the Saudi consulate in Istanbul on Oct 2, as well as the latest corporate earnings season.