US 10-year yields, which move inversely with prices, climbed 8 basis points, the largest daily rise since mid-May. US 30-year yields also had a significant gain, up nearly 8 basis points on the day, the most in two weeks as well.
US non-farm payrolls increased by 223,000 jobs last month, data on Friday showed. Data for March and April was revised to show the economy creating 15,000 more jobs than previously reported.
Also average hourly earnings rose eight cents, or 0.3 percent last month after edging up 0.1 percent in April, suggesting inflation was creeping higher.
"The Fed didn't need a report nearly this strong for them to have continued on course, a report like this is sort of icing on the cake," said Tom Porcelli, chief US economist, RBC Capital Markets in New York.
"The hurdle for the Fed is a lot lower than what the report gave us today. We've always been thinking four hikes (this year) ... but I think numbers like this might encourage people to reconsider the idea of four full hikes this year," he added.
US yields also extended their gains after upbeat US construction spending data and a higher-than-expected manufacturing index for the month of May.
Following Friday's data, traders overall remained quite confident of rate increases in June and September, prices of short-term interest-rate futures show, and they see about a 36 percent chance of a rate hike in December, up from about 32 percent before the employment report. Traders also increased bets on further rate increases in 2019.
The Fed has raised rates once this year so far in March and is widely expected to tighten again at this month's monetary policy meeting.
In mid-morning trading, US 10-year yields rose 2.905 percent, from Thursday's 2.822 percent.
US 30-year yields also advanced to 3.058 percent , compared with 2.985 percent late Thursday.
US two-year yields, meanwhile were likewise up at 2.479 percent, from 2.411 percent on Thursday.