kept their focus on developments surrounding the United Kingdom's exit from the European Union while digesting reports about a thawing in U.S.-China trade relations.

The benchmark 10-year yield traded at 2.877 percent while the short-term 2-year yield climbed to 2.77 percent. Bond yields move inversely to prices.

Bloomberg News reported earlier on Tuesday that China is moving toward cutting tariffs on cars made in the U.S. to . The proposal has been submitted to the Chinese Cabinet and will be reviewed in the coming days, the report said. A U.S. official later told Reuters that China indicated it will cut the tariffs, but the U.S. would wait on formal documentation and timing.

President Donald Trump also tweeted the administration was having "very productive conversations going on with China," adding: "Watch for some important announcements."

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Meanwhile, Chinese Vice Premier Liu reportedly said Tuesday that he had been in discussion with U.S. Treasury Secretary Steven Mnuchin and Trade Representative Robert Lighthizer, with the aim of de-escalating a global trade war.

The rise in yields was kept in chedk, however, as sentiment around the United Kingdom's proposed Brexit deal remained fragile. Prime Minister Theresa May abruptly postponed a parliamentary vote on Monday, sending sterling down to 20-month lows.

May headed to Brussels following the vote delay to seek more concessions from the European Union on the Brexit deal. However, European Commission President Jean-Claude Juncker said: "The deal we have achieved is the best deal possible, it is the only deal possible."

"There is no room whatsoever for renegotiation," Juncker told EU lawmakers, adding that there is however room to "give further clarification" on what the deal actually says.

—CNBC's Fred Imbert and Silvia Amaro contributed to this report.