US 10-year and 30-year yields fell to three-week lows, while those on two-year notes slid to two-week troughs.

Trump called his latest move retaliation for China's decision to raise tariffs on $50 billion in US goods, which came after Trump announced similar tariffs on Chinese goods on Friday.

"This trade war is driving the risk-off mode," said Gennadiy Goldberg, interest rates strategist, at TD Securities in New York.

US benchmark 10-year yields fell to a three-week low of 2.853 percent, from Monday's 2.926 percent. They were last at 2.878 percent.

US 30-year yields dropped to 2.991 percent, a three-week low as well, compared with 3.055 percent on Monday, and were last at 3.014 percent.

On the short end of the curve, US two-year yields sank to a two-week low of 2.496 percent, compared with 2.558 percent late on Monday. Two-year yields last traded at 2.524 percent.

The yield curve, meanwhile, continued to steepen on Tuesday, at least with respect to the spread between US 5-year notes and 30-year bonds. That spread narrowed to 26.90 basis points .

"A bull steepener is totally expected because a trade war is said to cause stagflation, which could prevent the Federal Reserve from further hiking rates," said TD's Goldberg.