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The three-month yield fell to minus 0.036%, an all-time low, while the one-month yield fell to minus 0.013% in mid-morning trading.
Short-term yields, which broadly reflect the federal funds rate, have fallen dramatically since the Federal Reserve cut its key interest rate to nearly zero earlier this month to combat the economic effects of the coronavirus pandemic.
As the disease has roiled financial markets, U.S. government debt has seen yields fall and prices rise as investors have sought safety in high-quality bonds.
Negative rates have been recorded on European and Japanese government bonds for several years.