Benchmark 10-year Treasury yields rose to trade at 2.2225 percent on Tuesday, breaking above 2.2 percent for the first time since September 22. They closed at 2.185 percent on Monday.
Meanwhile, yields on the 30-year Treasury rose to 3.0014 percent Tuesday, marking the first time since September it trades at a 3-handle. On Monday, it closed at 2.957 percent in the previous session.
Data releases due on Tuesday included September factory orders, which fell 1 percent, more than the expected 0.9 percent fall, and vehicle sales.
Stocks kicked off the first trading day of November with solid gains that took major averages to key levels. The Dow Jones Industrial Average closed in the green for 2015, joining the S&P 500 and the Nasdaq composite in positive territory for the year so far.
The S&P 500 gained more than 1 percent to top 2,100 points.
U.S. equities traded higher on Tuesday.
As well as data releases this week, markets will be keeping an eye on Fed commentary, as numerous Federal Open Market Committee members are due to speak, including Yellen, Vice Chair Stanley Fischer and New York Fed President William Dudley on Wednesday.
Traders will look for any hints on the timing and pace of an interest rate rise in the U.S.
Correction: This article has been updated to reflect that the 30-year bond yields broke above 3 percent for the first time since September.