The benchmark 10-year yield fell as much as 10 basis points Tuesday to 2.06%, the lowest level so far this year. That puts Treasuries on track for their sharpest daily rally since May, according to Bloomberg data. 

The move in the bond market comes as tensions between the U.S. and North Korea escalated on renewed concerns over nuclear war. Adding to global turmoil is Hurricane Irma, set to hit the southeast hard toward the end of this week as the region is still recovering from Hurricane Harvey's devastation. Traders have also looked to a risk-laden Washington, where prospects of a Fed rate hike become less likely and Congress works to avoid a government shutdown.

U.S. Treasuries hit new lows Tuesday around 1 p.m. ET after the auction of four-week bills set to mature October 5, close to when traders expect the government will exhaust the "extraordinary measures" it's used to stay below the debt limit. Those bills' rate was 1.3%, which is the highest for the maturity since 2008, according to Bloomberg data.

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