Government bond yields fell Thursday amid cooling expectations of an interest rate increase by the U.S. Federal Reserve.

Fed governor Christopher Waller said during a virtual event hosted by Reuters that he would support holding interest rates steady if August inflation data backs it up.

The remarks come a day after New York Fed President John Williams indicated that data so far isn't enough to warrant an increase in borrowing costs, prompting a reversal in yield rises.

Besides dovish remarks by Fed officials, fresh data indicated the U.S job market remains lukewarm ahead of the August payrolls report due Friday, further weakening the prospect of a Fed hike.

The 10-year U.S. Treasury yield recently traded at 4.754%, down from 4.781% overnight, according to LSEG. Earlier this week, it reached a 33-month high.

In Europe, the 10-year German Bund yield fell 2.5 basis points to 3.354%, after hitting a 15-year high of 3.395% on Wednesday. The 10-year U.K. gilt yield declined 8.2 basis points to 5.157%, down from Wednesday's 19-year peak of 5.294%.

U.S. money markets now price a 56% probability of a rate hike this month, down from nearly 70% on Wednesday, LSEG data showed.

The decline in yields was accompanied by a weakening of the dollar. The WSJ Dollar Index fell 0.5%, as the greenback dropped 2% against the Japanese yen.

However, the selloff in bonds that pushed yields to recent highs might not be over, as some of the factors that drove it remained in place.

After a small decline Wednesday, crude prices recovered Thursday. Brent was up 1.3%, to $96.88, keeping alive inflation concerns that may result in higher interest rates.

Yields have more room to rise due to multiple unresolved issues, conflicts, and no clear resolution timeline anywhere, ​CIFC Asset Management managing director Natalia Lojevsky said in a note.

"You have two stresses hitting bond markets around the globe at the same time: a structural supply problem from deficits and massive issuance rates of corporate and sovereign​," she said.

That combination explains the recent jump in yields and why it has been relatively aggressive, she said.

Friday's employment data will be a key input into market expectations about the Fed's decision at the Sept. 16 meeting. Job creation is expected to rebound to 53,000 from a 23,000 loss in July, according to economists polled by The Wall Street Journal, still a relatively slow pace.

"When we triangulate across all the labor market data that will be released this week, we're expecting that the labor market will be room temperature, rather than boiling or frozen. And that would be good news for the Fed," Russell Investments' senior investment strategist BeiChen Lin said in a note.

However, if job creation were to come in significantly stronger than consensus expectations, "that might cause the Fed to give more consideration to rate hikes if inflation does not cooperate," he said.