The 10- and 2-year U.S. Treasury yields fell on Tuesday as markets reopened after being closed for Memorial Day on Monday and investors braced themselves for a vote on a debt ceiling deal ahead of the June 5 deadline.

The yield on the 10-year Treasury was down by almost 13 basis points to 3.692%. The 2-year Treasury was trading almost 13 basis points lower at 4.463%.

Yields and prices move in opposite directions and one basis point equals 0.01%.

Over the weekend, President Joe Biden and House Speaker Kevin McCarthy reached an agreement to raise the debt ceiling. That came after Treasury Secretary Janet Yellen said Friday that the U.S. would default on its debt obligations as early as June 5, several days later than the previous June 1 deadline.

A vote on the deal is expected to take place Wednesday in the Republican-controlled House of Representatives and later in the week in the Senate, which is controlled by the Democrats. A group of Republicans said Monday they would not agree to the deal, suggesting that there was a way to go before it is approved.

However, politicians from both sides of the aisle said they expected a resolution to be found and analysts appeared positive about a deal being approved ahead of the deadline.

Elsewhere, investors digested April's personal consumption expenditures price index that on Friday came in at 0.4% on a monthly basis which was higher than expected. The index is the Federal Reserve's preferred inflation gauge.

That comes as uncertainty grows over the Fed's interest rate policy and whether officials would hike rates further in their battle against persistent inflation.

A series of jobs data is expected throughout the week and could provide fresh hints about the state of the U.S. economy, which may also affect monetary policy.