Benchmark US 10-year, 30-year, and two-year yields fell to their lowest since Nov. 2.

The Treasury market was closed on Monday for the Veterans Day holiday.

"If oil prices decline that should leave less inflation because the cost of energy is lower and so you would expect lower interest rates all else being equal," said Jon Hill, vice president of US fixed income strategy at BMO Capital Markets in New York.

US crude oil futures were on track to close lower for a record 12th straight session, down 6.5 percent at $56.06 per barrel. Tuesday's sell-off was the worst yet.

But the decline in yields amid the oil downdraft has been mitigated somewhat, analysts said, by news that Britain struck a draft divorce deal with the European Union after more than a year of talks.

Along with the positive Brexit news, the recovery on Wall Street shares after a steep sell-off on Monday has also helped limit the fall in yields.

In afternoon trading, benchmark 10-year note yields fell to 3.150 percent from 3.189 percent late on Friday. Ten-year yields earlier fell to 3.143 percent, a more than one-week low.

US 30-year yields were at 3.373 percent, compared with Friday's 3.392 percent.

On the short end of the curve, US two-year yields declined to 2.895 percent, from 2.932 percent on Friday.

This week, the market is looking at US consumer prices and retail sales on the economic data front.

US core CPI is expected to have risen slightly to 0.2 percent in October, from 0.1 percent the previous month.

Michael Pearce, senior US economist at Capital Economics, believes US core inflation may have already peaked.

"The modest growth of unit labor costs and the appreciation of the dollar this year suggest that core inflation is unlikely to rise much further," wrote Pearce in a research note.

"With inflation quiescent, we expect the Fed to continue raising interest rates gradually and to move quickly to the sidelines next year as economic growth slows below potential," he added.